scalation
API
Generated with
scalation/scalation/scalation.modeling

scalation.modeling

package scalation.modeling

Members list

Packages

package scalation.modeling.classifying
package scalation.modeling.clustering
package scalation.modeling.forecasting
package scalation.modeling.neuralnet

Type members

Classlikes

case class AFF(name: String, f: FunctionS2S, f_: FunctionV2V, d: FunctionV2V, bounds: (Double, Double), arange: (Double, Double))

The AFF class holds an Activation Function Family (AFF).

The AFF class holds an Activation Function Family (AFF).

Value parameters

arange

the (lower, upper) bounds on the input (active) range of the activation function e.g., (-2, 2) for sigmoid, defaults to null => no limit

bounds

the (lower, upper) bounds on the output range of the activation function, e.g., (0, 1) for sigmoid, defaults to null => no limit

d

the vector version of the activation function derivative

f

the activation function itself (scalar version)

f_

the vector version of the activation function

name

the name of the activation function

Attributes

Supertypes
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
object ActivationFun

The ActivationFun object contains common Activation functions and provides both scalar and vector versions.

The ActivationFun object contains common Activation functions and provides both scalar and vector versions.

Attributes

See also
Supertypes
class Object
trait Matchable
class Any
Self type
object DistanceOutlier extends Outlier

Detect outliers in the vector by treating anything that falls outside of some distance from the mean as an outlier. Common number of standard deviation units are 2.5, 2.7, 3 and 3.5. The larger the dataset, the greater the number of units that should be used.

Detect outliers in the vector by treating anything that falls outside of some distance from the mean as an outlier. Common number of standard deviation units are 2.5, 2.7, 3 and 3.5. The larger the dataset, the greater the number of units that should be used.

Attributes

Supertypes
trait Outlier
class Object
trait Matchable
class Any
Self type
object Example_AutoMPG

The Example_AutoMPG object stored the UCI AutoMPG dataset in a matrix.

The Example_AutoMPG object stored the UCI AutoMPG dataset in a matrix.

Attributes

See also

archive.ics.uci.edu/ml/datasets/Auto+MPG

Supertypes
class Object
trait Matchable
class Any
Self type
object Example_BPressure

The Example_BPressure object stores the Blood Pressure dataset in a matrix.

The Example_BPressure object stores the Blood Pressure dataset in a matrix.

Attributes

See also

online.stat.psu.edu/online/development/stat501/data/bloodpress.txt

Supertypes
class Object
trait Matchable
class Any
Self type
object Example_BasketBall

The Example_BasketBall class stores a medium-sized example dataset with data about basketball player that can be used to predict their scoring average.

The Example_BasketBall class stores a medium-sized example dataset with data about basketball player that can be used to predict their scoring average.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
class ExpRegression(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter, nonneg: Boolean) extends Predictor, Fit

The ExpRegression class supports exponential regression. In this case, x is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector b in the exponential regression equation log (mu (x)) = b dot x = b_0 + b_1 * x_1 + ... b_k * x_k

The ExpRegression class supports exponential regression. In this case, x is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector b in the exponential regression equation log (mu (x)) = b dot x = b_0 + b_1 * x_1 + ... b_k * x_k

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (currently none)

nonneg

whether to check that responses are nonnegative (defaults to true)

x

the data/input matrix

y

the response/output vector

Attributes

See also
Companion
object
Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object ExpRegression

The ExpRegression companion object provides factory methods for creating exponential regression models.

The ExpRegression companion object provides factory methods for creating exponential regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
trait ExpandableVariable

The ExpandableVariable trait provides the framwork for replacing categorical variables with dummy variables. A dummy variable having nl levels is replaced with nl-1 dummy variables.

The ExpandableVariable trait provides the framwork for replacing categorical variables with dummy variables. A dummy variable having nl levels is replaced with nl-1 dummy variables.

Attributes

Supertypes
class Object
trait Matchable
class Any
Known subtypes
object Fit

The Fit companion object provides factory methods for assessing quality of fit for standard types of modeling techniques.

The Fit companion object provides factory methods for assessing quality of fit for standard types of modeling techniques.

Attributes

Companion
trait
Supertypes
class Object
trait Matchable
class Any
Self type
Fit.type
trait Fit(var dfm: Double, var df: Double) extends FitM

The Fit trait provides methods to determine basic Quality of Fit QoF measures.

The Fit trait provides methods to determine basic Quality of Fit QoF measures.

Value parameters

df

the degrees of freedom for error

dfm

the degrees of freedom for model/regression

Attributes

See also

reset to reset the degrees of freedom

Companion
object
Supertypes
trait FitM
class Object
trait Matchable
class Any
Known subtypes
class AR1MA
class CNN_1D
class ELM_3L1
class NeuralNet_2L
class NeuralNet_3L
class NeuralNet_XL
class RegressionMV
class FitI
class AR
class ARMA
class ARIMA
class SARIMA
class SARIMAX
class NullModel
class QuadSpline
class RandomWalk
class TrendModel
class NullModel
class Perceptron
class Regression
class ARX
class ARX_Quad
class TestFit
Show all
object FitI

The FitI companion object provides factory methods for assessing quality of fit for standard types of modeling techniques.

The FitI companion object provides factory methods for assessing quality of fit for standard types of modeling techniques.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
FitI.type
class FitI(dfm_: Double, df_: Double) extends Fit

The FitI class provides methods to determine Interval-based Quality of Fit QoFI metrics/measures.

The FitI class provides methods to determine Interval-based Quality of Fit QoFI metrics/measures.

Value parameters

df

the degrees of freedom for error

dfm

the degrees of freedom for model/regression

Attributes

See also

reset to reset the degrees of freedom

Companion
object
Supertypes
trait Fit
trait FitM
class Object
trait Matchable
class Any
Known subtypes
class AR
class ARMA
class ARIMA
class SARIMA
class SARIMAX
class NullModel
class QuadSpline
class RandomWalk
class TrendModel
Show all
trait FitM

The FitM class provides methods to determine basic Quality of Fit 'QoF' metrics/measures suitable for all Models. Note, to work with multiple types of models where degrees of freedom (df) may be hard to calculate, sde uses m-1 rather than df for sample estimates, while rmse uses a population formula (i.e., divide by m). Therefore, in ScalaTion sde will be slightly larger than rmse.

The FitM class provides methods to determine basic Quality of Fit 'QoF' metrics/measures suitable for all Models. Note, to work with multiple types of models where degrees of freedom (df) may be hard to calculate, sde uses m-1 rather than df for sample estimates, while rmse uses a population formula (i.e., divide by m). Therefore, in ScalaTion sde will be slightly larger than rmse.

Attributes

Companion
object
Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait FitC
class BaggingTrees
class RandomForest
class HiddenMarkov
class NaiveBayes
class NaiveBayesR
class NullModel
class SimpleLDA
class TANBayes
trait Fit
class AR1MA
class CNN_1D
class ELM_3L1
class NeuralNet_2L
class NeuralNet_3L
class NeuralNet_XL
class RegressionMV
class FitI
class AR
class ARMA
class ARIMA
class SARIMA
class SARIMAX
class NullModel
class QuadSpline
class RandomWalk
class TrendModel
class NullModel
class Perceptron
class Regression
class ARX
class ARX_Quad
class TestFit
Show all
object FitM

The FitM object provides functions for making fit maps for QoF measures.

The FitM object provides functions for making fit maps for QoF measures.

Attributes

Companion
trait
Supertypes
class Object
trait Matchable
class Any
Self type
FitM.type
trait Imputation

The Imputation trait specifies an imputation operation called impute to be defined by the objects implementing it, i.e., ImputeRegression - impute missing values using SimpleRegression ImputeForward - impute missing values using previous values and slopes ImputeBackward - impute missing values using subsequent values and slopes ImputeMean - impute missing values usind the filtered mean ImputeNormal - impute missing values using the median of Normal random variates ImputeMovingAvg - impute missing values using the moving average ImputeNormalWin - impute missing values using the median of Normal random variates for a window

The Imputation trait specifies an imputation operation called impute to be defined by the objects implementing it, i.e., ImputeRegression - impute missing values using SimpleRegression ImputeForward - impute missing values using previous values and slopes ImputeBackward - impute missing values using subsequent values and slopes ImputeMean - impute missing values usind the filtered mean ImputeNormal - impute missing values using the median of Normal random variates ImputeMovingAvg - impute missing values using the moving average ImputeNormalWin - impute missing values using the median of Normal random variates for a window

Attributes

Supertypes
class Object
trait Matchable
class Any
Known subtypes
object ImputeForward
object ImputeMean
object ImputeNormal
Show all
object ImputeBackward extends Imputation

The ImputeBackward object imputes missing values using the subsequent value and slope.

The ImputeBackward object imputes missing values using the subsequent value and slope.

Attributes

Supertypes
trait Imputation
class Object
trait Matchable
class Any
Self type
object ImputeForward extends Imputation

The ImputeForward object imputes missing values using the previous value and slope.

The ImputeForward object imputes missing values using the previous value and slope.

Attributes

Supertypes
trait Imputation
class Object
trait Matchable
class Any
Self type
object ImputeMean extends Imputation

The ImputeMean object imputes missing values using the filtered mean.

The ImputeMean object imputes missing values using the filtered mean.

Attributes

Supertypes
trait Imputation
class Object
trait Matchable
class Any
Self type
ImputeMean.type
object ImputeMovingAvg extends Imputation

The ImputeMovingAvg object imputes missing values using the moving average.

The ImputeMovingAvg object imputes missing values using the moving average.

Attributes

Supertypes
trait Imputation
class Object
trait Matchable
class Any
Self type
object ImputeNormal extends Imputation

The ImputeNormal object imputes missing values using the median Normal variates.

The ImputeNormal object imputes missing values using the median Normal variates.

Attributes

Supertypes
trait Imputation
class Object
trait Matchable
class Any
Self type
object ImputeNormalWin extends Imputation

The ImputeNormalWin object imputes the missing values in the vector using Normal Distribution for a sliding window.

The ImputeNormalWin object imputes the missing values in the vector using Normal Distribution for a sliding window.

Attributes

Supertypes
trait Imputation
class Object
trait Matchable
class Any
Self type
object ImputeRegression extends Imputation

The ImputeRegression object imputes missing values using SimpleRegression.

The ImputeRegression object imputes missing values using SimpleRegression.

Attributes

Supertypes
trait Imputation
class Object
trait Matchable
class Any
Self type
object Initializer

The Initializer object provides functions to initialize the parameters/weights of Neural Networks. Supports Uniform, Normal and Nguyen & Widrow methods.

The Initializer object provides functions to initialize the parameters/weights of Neural Networks. Supports Uniform, Normal and Nguyen & Widrow methods.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
class KNN_Regression(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter) extends Predictor, Fit

The KNN_Regression class is used to predict a response value for new vector z. It works by finding its kappa nearest neighbors. These neighbors essentially vote according to their prediction. The consensus is the average individual predictions for z. Using a distance metric, the kappa vectors nearest to z are found in the training data, which are stored row-wise in data matrix x. The corresponding response values are given in the vector y, such that the response value for vector x(i) is given by y(i). WARNING: in-sample testing is only meaningful for large values of hyper-parsameter kappa

The KNN_Regression class is used to predict a response value for new vector z. It works by finding its kappa nearest neighbors. These neighbors essentially vote according to their prediction. The consensus is the average individual predictions for z. Using a distance metric, the kappa vectors nearest to z are found in the training data, which are stored row-wise in data matrix x. The corresponding response values are given in the vector y, such that the response value for vector x(i) is given by y(i). WARNING: in-sample testing is only meaningful for large values of hyper-parsameter kappa

Value parameters

fname_

the names for all features/variables (defaults to null)

hparam

the number of nearest neighbors to consider (defaults to KNN_Regression.hp)

x

the vectors/points of predictor data stored as rows of a matrix

y

the response value for each vector in x

Attributes

Companion
object
Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object KNN_Regression

The KNN_Regression companion object provides factory methods for creating k-nearest neighbor regression models.

The KNN_Regression companion object provides factory methods for creating k-nearest neighbor regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class LassoRegression(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter) extends Predictor, Fit

The LassoRegression class supports multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the regression equation y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e where 'e' represents the residuals (the part not explained by the model).

The LassoRegression class supports multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the regression equation y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e where 'e' represents the residuals (the part not explained by the model).

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the shrinkage hyper-parameter, lambda (0 => OLS) in the penalty term 'lambda * b dot b'

x

the data/input m-by-n matrix

y

the response/output m-vector

Attributes

See also

see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

Companion
object
Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object LassoRegression

The LassoRegression companion object provides factory methods for the LassoRegression class.

The LassoRegression companion object provides factory methods for the LassoRegression class.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
trait Model

The Model trait provides a common framework for all models and serves as base trait for Classifier, Forecaster, Predictor, and PredictorMV traits. The train and test methods must be called first, e.g., val model = NullModel (y) model.train (null, y) model.test (null, y)

The Model trait provides a common framework for all models and serves as base trait for Classifier, Forecaster, Predictor, and PredictorMV traits. The train and test methods must be called first, e.g., val model = NullModel (y) model.train (null, y) model.test (null, y)

Attributes

Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait Classifier
class BaggingTrees
class RandomForest
class HiddenMarkov
class NaiveBayes
class NaiveBayesR
class NullModel
class SimpleLDA
class TANBayes
trait Forecaster
class AR
class AR1MA
class ARMA
class ARIMA
class SARIMA
class SARIMAX
class NullModel
class QuadSpline
class RandomWalk
class TrendModel
trait PredictorMV
class CNN_1D
class NeuralNet_2L
class NeuralNet_3L
class NeuralNet_XL
class RegressionMV
trait Predictor
class ELM_3L1
class NullModel
class Perceptron
class Regression
class ARX
class ARX_Quad
Show all
trait MonitorLoss

The MonitorLoss trait provides methods to track the converegence of the of optimization algorithms based on the value of the loss function.

The MonitorLoss trait provides methods to track the converegence of the of optimization algorithms based on the value of the loss function.

Attributes

Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait Optimizer
class Perceptron
trait NoSubModels

The NoSubModel trait is for modeling techniques that do not support building sub-models/feature selection (adding/remove variables from the model). For example, SimpleRegression only has one feature/predictor variable, so feature selection makes no sense for this modeling technique.

The NoSubModel trait is for modeling techniques that do not support building sub-models/feature selection (adding/remove variables from the model). For example, SimpleRegression only has one feature/predictor variable, so feature selection makes no sense for this modeling technique.

Attributes

Supertypes
class Object
trait Matchable
class Any
Known subtypes
class NullModel
case class Node(j: Int, branch: Int, b: VectorD, thresh: Double, depth: Int, pthresh: Double, pfea: Int, leaf: Boolean)

The Node class contains information for a tree node.

The Node class contains information for a tree node.

Value parameters

b

leaf node's prediction parameters (b0 for mean or b for regression)

branch

the branch value (0 => left, 1 => right)

depth

the current depth of the node

j

the feature/variable of the node used for splitting, if it is leaf, contains the feature of its parent

leaf

whether the node is a leaf node

pfea

the feature of parent node

pthresh

the threshold for parent node

thresh

the threshold for continuous feature

Attributes

Supertypes
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
class NonlinearRegression(x: MatrixD, y: VectorD, f: FunctionP2S, b_init: VectorD, fname_: Array[String], hparam: HyperParameter) extends Predictor, Fit, NoSubModels

The NonlinearRegression class supports Nonlinear Regression. In this case, x can be multi-dimensional [1, x1, ... xk] and the function f is nonlinear in the parameters b. Fit the parameter vector b in the regression equation y = f(x, b) + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector b by using Nonlinear Programming to minimize sum of squared errors (sse).

The NonlinearRegression class supports Nonlinear Regression. In this case, x can be multi-dimensional [1, x1, ... xk] and the function f is nonlinear in the parameters b. Fit the parameter vector b in the regression equation y = f(x, b) + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector b by using Nonlinear Programming to minimize sum of squared errors (sse).

Value parameters

b_init

the initial guess for the parameter vector b

f

the nonlinear function f(x, b) to fit

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (currently has none)

x

the data/input matrix augmented with a first column of ones

y

the response/output vector

Attributes

See also
Companion
object
Supertypes
trait NoSubModels
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object NonlinearRegression

The NonlinearRegression companion object provides factory methods for buidling Nonlinear Regression models.

The NonlinearRegression companion object provides factory methods for buidling Nonlinear Regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class NullModel(y: VectorD) extends Predictor, Fit, NoSubModels

The NullModel class implements the simplest type of predictive modeling technique that just predicts the response y to be the mean. Fit the parameter vector b in the null regression equation

The NullModel class implements the simplest type of predictive modeling technique that just predicts the response y to be the mean. Fit the parameter vector b in the null regression equation

y  =  b dot x + e  =  b0 + e

where e represents the residual/error vector (the part not explained by the model).

Value parameters

y

the response/output vector

Attributes

Companion
object
Supertypes
trait NoSubModels
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object NullModel

The NullModel companion object provides a simple factory method for building null models.

The NullModel companion object provides a simple factory method for building null models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
NullModel.type
trait Outlier

The Outlier trait specifies an outlier detection operation to be defined by the objects implementing it, i.e., DistanceOutlier - outlier = beyond 'STDEV_CUTOFF' units from mean QuantileOutlier - outlier = in the 'PERCENTILE' tails of the distribution QuartileOutlier - outlier = 'X_MULTIPLIER' times beyond the middle two quartiles Leaving extreme values in datasets that are highly unlikely to represent legitimate values will reduce the quality of models. However, removing legitimate extreme values will only make the model appear to be good, and it may fail in the real world.

The Outlier trait specifies an outlier detection operation to be defined by the objects implementing it, i.e., DistanceOutlier - outlier = beyond 'STDEV_CUTOFF' units from mean QuantileOutlier - outlier = in the 'PERCENTILE' tails of the distribution QuartileOutlier - outlier = 'X_MULTIPLIER' times beyond the middle two quartiles Leaving extreme values in datasets that are highly unlikely to represent legitimate values will reduce the quality of models. However, removing legitimate extreme values will only make the model appear to be good, and it may fail in the real world.

Attributes

See also

Imputation as an alternative to removal of outliers

Supertypes
class Object
trait Matchable
class Any
Known subtypes
class Perceptron(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter, f: AFF, val itran: FunctionV2V) extends Predictor, Fit, MonitorLoss

The Perceptron class supports single-output, 2-layer (input and output) Neural-Networks. Although perceptrons are typically used for classification, this class is used for prediction. Given several input vectors and output values (training data), fit the weights/parameters b connecting the layers, so that for a new input vector z, the net can predict the output value, i.e., z = f (b dot z) The parameter vector b (w) gives the weights between input and output layers. Note, b0 is treated as the bias, so x0 must be 1.0.

The Perceptron class supports single-output, 2-layer (input and output) Neural-Networks. Although perceptrons are typically used for classification, this class is used for prediction. Given several input vectors and output values (training data), fit the weights/parameters b connecting the layers, so that for a new input vector z, the net can predict the output value, i.e., z = f (b dot z) The parameter vector b (w) gives the weights between input and output layers. Note, b0 is treated as the bias, so x0 must be 1.0.

Value parameters

f

the activation function family for layers 1->2 (input to output)

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters for the model/network (defaults to Perceptron.hp)

itran

the inverse transformation function returns responses to original scale

x

the data/input m-by-n matrix (data consisting of m input vectors)

y

the response/output m-vector (data consisting of m output values)

Attributes

Companion
object
Supertypes
trait MonitorLoss
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object Perceptron extends Scaling

The Perceptron companion object provides factory methods for creating perceptrons.

The Perceptron companion object provides factory methods for creating perceptrons.

Attributes

Companion
class
Supertypes
trait Scaling
class Object
trait Matchable
class Any
Self type
Perceptron.type
class PoissonRegression(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter) extends Predictor, Fit

The PoissonRegression class supports Poisson regression. In this case, x may be multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the Poisson regression equation log (mu(x)) = b dot x = b_0 + b_1 * x_1 + ... b_k * x_k where e represents the residuals (the part not explained by the model) and y is now integer valued.

The PoissonRegression class supports Poisson regression. In this case, x may be multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the Poisson regression equation log (mu(x)) = b dot x = b_0 + b_1 * x_1 + ... b_k * x_k where e represents the residuals (the part not explained by the model) and y is now integer valued.

Value parameters

fname_

the names of the features/variables (defaults to null)

hparam

the hyper-parameters (currently has none)

x

the data/input matrix augmented with a first column of ones

y

the integer response/output vector, y_i in {0, 1, ... }

Attributes

See also

see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

Companion
object
Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object PoissonRegression

The PoissonRegression companion object provides factory methods for creating Poisson regression models.

The PoissonRegression companion object provides factory methods for creating Poisson regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class PolyORegression(t: MatrixD, y: VectorD, ord: Int, fname_: Array[String], hparam: HyperParameter) extends Regression

The PolyORegression class supports orthogonal polynomial regression. In this case, 't' is expanded to an orthononalization of '[1, t, t^2 ... t^k]'. Fit the parameter vector 'b' in the regression equation

The PolyORegression class supports orthogonal polynomial regression. In this case, 't' is expanded to an orthononalization of '[1, t, t^2 ... t^k]'. Fit the parameter vector 'b' in the regression equation

y  =  b dot x + e  =  b_0 + b_1 * t +  b_2 * t^2 ... b_k * t^k + e

where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve for the parameter vector 'b' using the Normal Equations: x.t * x * b = x.t * y b = fac.solve (.)

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (defaults to PolyRegression.hp)

ord

the order (k) of the polynomial (max degree)

t

the initial data/input m-by-1 matrix: t_i expands to x_i = [1, t_i, t_i^2, ... t_i^k]

y

the response/ouput vector

Attributes

See also
Companion
object
Supertypes
class Regression
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object PolyORegression

The PolyORegression companion object provides factory methods for creating orthogonal polynomial regression models and methods for creating functional forms.

The PolyORegression companion object provides factory methods for creating orthogonal polynomial regression models and methods for creating functional forms.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class PolyRegression(t: MatrixD, y: VectorD, ord: Int, fname_: Array[String], hparam: HyperParameter) extends Regression

The PolyRegression class supports polynomial regression. In this case, t is expanded to [1, t, t^2 ... t^k]. Fit the parameter vector b in the regression equation y = b dot x + e = b_0 + b_1 * t + b_2 * t^2 ... b_k * t^k + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve for the parameter vector b using the Normal Equations: x.t * x * b = x.t * y b = fac.solve (.)

The PolyRegression class supports polynomial regression. In this case, t is expanded to [1, t, t^2 ... t^k]. Fit the parameter vector b in the regression equation y = b dot x + e = b_0 + b_1 * t + b_2 * t^2 ... b_k * t^k + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve for the parameter vector b using the Normal Equations: x.t * x * b = x.t * y b = fac.solve (.)

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (defaults to PolyRegression.hp)

ord

the order (k) of the polynomial (max degree)

t

the initial data/input m-by-1 matrix: t_i expands to x_i = [1, t_i, t_i^2, ... t_i^k]

y

the response/ouput vector

Attributes

See also
Companion
object
Supertypes
class Regression
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object PolyRegression

The PolyRegression companion object provides factory methods for creating

The PolyRegression companion object provides factory methods for creating

  • polynomial regression models and methods for creating functional forms.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
trait Predictor(x: MatrixD, y: VectorD, var fname: Array[String], hparam: HyperParameter) extends Model

The Predictor trait provides a framwork for multiple predictive analytics techniques, e.g., Regression. x is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector b in for example the regression equation y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e

The Predictor trait provides a framwork for multiple predictive analytics techniques, e.g., Regression. x is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector b in for example the regression equation y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e

Value parameters

fname

the feature/variable names (if null, use x_j's)

hparam

the hyper-parameters for the model

x

the input/data m-by-n matrix (augment with a first column of ones to include intercept in model)

y

the response/output m-vector

Attributes

Companion
object
Supertypes
trait Model
class Object
trait Matchable
class Any
Known subtypes
class ELM_3L1
class NullModel
class Perceptron
class Regression
class ARX
class ARX_Quad
Show all
object Predictor

The Predictor companion object provides a method for testing predictive models.

The Predictor companion object provides a method for testing predictive models.

Attributes

Companion
trait
Supertypes
class Object
trait Matchable
class Any
Self type
Predictor.type
enum QoF(val name: String)

The QoF enum defines the Quality of Fit (QoF) measures/metrics.

The QoF enum defines the Quality of Fit (QoF) measures/metrics.

Value parameters

name

the name of the parameter

Attributes

Supertypes
trait Enum
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
enum QoFI(val name: String)

The QoFI enum defines the Interval-based Quality of Fit (QoFI) measures/metrics.

The QoFI enum defines the Interval-based Quality of Fit (QoFI) measures/metrics.

Value parameters

name

the name of the parameter

Attributes

Supertypes
trait Enum
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
object QuantileOutlier extends Outlier

Detect outliers in the vector by treating anything that falls outside 1-st or 99-th percentile. Common percentiles that may be passed in factor are .0035, .005, .01, .02, and .05. Note, extreme 2% as discussed in textbook corresponds to 1% in left tail and 1% in right tail.

Detect outliers in the vector by treating anything that falls outside 1-st or 99-th percentile. Common percentiles that may be passed in factor are .0035, .005, .01, .02, and .05. Note, extreme 2% as discussed in textbook corresponds to 1% in left tail and 1% in right tail.

Attributes

Supertypes
trait Outlier
class Object
trait Matchable
class Any
Self type
object QuartileXOutlier extends Outlier

Detect outliers in the vector by treating anything that falls below the 1st Quartile or above the 3rd Quartile as an Outlier. Common values for X_MULTIPLIER are 1.5 and 2.0.

Detect outliers in the vector by treating anything that falls below the 1st Quartile or above the 3rd Quartile as an Outlier. Common values for X_MULTIPLIER are 1.5 and 2.0.

Attributes

Supertypes
trait Outlier
class Object
trait Matchable
class Any
Self type
class Regression(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter) extends Predictor, Fit

The Regression class supports multiple linear regression. In this case, x is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector b in the regression equation y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve the parameter vector b using the Normal Equations: x.t * x * b = x.t * y b = fac.solve (.) Five factorization algorithms are provided: Fac_QR QR Factorization: slower, more stable (default) Fac_SVD Singular Value Decomposition: slowest, most robust Fac_Cholesky Cholesky Factorization: faster, less stable (reasonable choice) Fac_LU' LU Factorization: better than InverseFac_Inverse` Inverse Factorization: textbook approach

The Regression class supports multiple linear regression. In this case, x is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector b in the regression equation y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve the parameter vector b using the Normal Equations: x.t * x * b = x.t * y b = fac.solve (.) Five factorization algorithms are provided: Fac_QR QR Factorization: slower, more stable (default) Fac_SVD Singular Value Decomposition: slowest, most robust Fac_Cholesky Cholesky Factorization: faster, less stable (reasonable choice) Fac_LU' LU Factorization: better than InverseFac_Inverse` Inverse Factorization: textbook approach

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (defaults to Regression.hp)

x

the data/input m-by-n matrix (augment with a first column of ones to include intercept in model)

y

the response/output m-vector

Attributes

See also

see.stanford.edu/materials/lsoeldsee263/05-ls.pdf Note, not intended for use when the number of degrees of freedom 'df' is negative.

Companion
object
Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
Known subtypes
class ARX
class ARX_Quad
Show all
object Regression

The Regression companion object provides factory methods for creating regression models.

The Regression companion object provides factory methods for creating regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
Regression.type
class RegressionCat(x_: MatrixD, t: MatrixI, y: VectorD, fname_: Array[String], hparam: HyperParameter) extends Regression, ExpandableVariable

The RegressionCat class supports Regression that contains Categorical Variables. somtimes called ANalysis of COVAriance (ANCOVA). It allows the addition of categorical (treatment) variables t into a multiple linear regression. This is done by introducing dummy variables dj to distinguish the treatment level. The problem is again to fit the parameter vector b in the augmented regression equation y = b dot x + e = b0 + b_1 * x_1 + b_2 * x_2 + ... b_k * x_k + b_k+1 * d_1 + b_k+2 * d_2 + ... b_k+l * d_l + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve for the parameter vector b using the Normal Equations: x.t * x * b = x.t * y b = fac.solve (.) t has categorical values/levels, e.g., treatment levels (0, ... t.max)

The RegressionCat class supports Regression that contains Categorical Variables. somtimes called ANalysis of COVAriance (ANCOVA). It allows the addition of categorical (treatment) variables t into a multiple linear regression. This is done by introducing dummy variables dj to distinguish the treatment level. The problem is again to fit the parameter vector b in the augmented regression equation y = b dot x + e = b0 + b_1 * x_1 + b_2 * x_2 + ... b_k * x_k + b_k+1 * d_1 + b_k+2 * d_2 + ... b_k+l * d_l + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve for the parameter vector b using the Normal Equations: x.t * x * b = x.t * y b = fac.solve (.) t has categorical values/levels, e.g., treatment levels (0, ... t.max)

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (defaults to Regression.hp)

t

the treatment/categorical variable matrix

x_

the data/input matrix of continuous variables

y

the response/output vector

Attributes

See also

see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

Companion
object
Supertypes
class Regression
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object RegressionCat

The RegressionCat companion object provides factory methods and other helper methods.

The RegressionCat companion object provides factory methods and other helper methods.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
object RegressionTree

The RegressionTree companion object is used to count the number of leaves and provide factory methods for creating regression trees.

The RegressionTree companion object is used to count the number of leaves and provide factory methods for creating regression trees.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class RegressionTree(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter, curDepth: Int, branchValue: Int, feature: Int, use_r_fb: Boolean, leaves: Counter) extends Predictor, Fit

The RegressionTree class implements a Regression Tree that recursively partitions the dataset (x, y) by finding a threshold for each feature/x-variable. The threshold for a feature is the value that minimizes sseL + sseR, the sum of the "sum of squared errors".

The RegressionTree class implements a Regression Tree that recursively partitions the dataset (x, y) by finding a threshold for each feature/x-variable. The threshold for a feature is the value that minimizes sseL + sseR, the sum of the "sum of squared errors".

Value parameters

branchValue

the branch value for the tree node (defaults to -1)

curDepth

current depth (defaults to 0)

feature

the feature for the tree's parent node (defaults to -1)

fname_

the names of the model's features/variables (defaults to null)

hparam

the hyper-parameters for the model (defaults to RegressionTree.hp)

leaves

the leaf counter (defaults to Counter ())

use_r_fb

whether to use (by regression tree) feature bagging (fb) i.e., use a subset of the features, @see RegressionTreeRF with parameter use_fb

x

the m-by-n input/data matrix

y

the output/response m-vector

Attributes

Companion
object
Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
class RegressionTreeGB(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter) extends Predictor, Fit

The RegressionTreeGB class uses Gradient Boosting using RegressionTrees.

The RegressionTreeGB class uses Gradient Boosting using RegressionTrees.

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters for the model (defaults to RegressionTree.hp)

x

the input/data matrix

y

the output/response vector

Attributes

Companion
object
Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object RegressionTreeGB

The RegressionTreeGB companion object defines hyper-parameters and provides a factory methods for creating gradient boosted regression trees.

The RegressionTreeGB companion object defines hyper-parameters and provides a factory methods for creating gradient boosted regression trees.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
object RegressionTreeMT

The RegressionTreeMT companion object is used to count the number of leaves and provide factory methods for creating regression model trees.

The RegressionTreeMT companion object is used to count the number of leaves and provide factory methods for creating regression model trees.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class RegressionTreeMT(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter, curDepth: Int, branchValue: Int, feature: Int, leaves: Counter) extends Predictor, Fit

The RegressionTreeMT class implements a Regression Tree (MT) that selects splitting features using minimal variance in children nodes. To avoid exponential choices in the selection, supporting ordinal features currently.

The RegressionTreeMT class implements a Regression Tree (MT) that selects splitting features using minimal variance in children nodes. To avoid exponential choices in the selection, supporting ordinal features currently.

Value parameters

branchValue

the branch value for the tree node (defaults to -1)

curDepth

current depth (defaults to 0)

feature

the feature for the tree's parent node (defaults to -1)

fname_

the names of the model's features/variables (defaults to null)

hparam

the hyper-parameters for the model (defaults to RegressionTree.hp)

leaves

the leaf counter (defaults to Counter ())

x

the m-by-n input/data matrix

y

the output/response m-vector

Attributes

Companion
object
Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
class RegressionTreeRF(x: MatrixD, y: VectorD, fname_: Array[String], use_fb: Boolean, hparam: HyperParameter) extends Predictor, Fit

The RegressionTreeRF class uses several randomly built reegression trees for prediction. It randomly selects sub-samples of 'bRatio * x.dim' size from the data x and y to build nTrees regression trees. The predict method uses the average over all trees. Note: By default this class does not select sub-features to build the trees (like Bagging Trees) Set use_fb (feature bagging) to true to turn this capability on

The RegressionTreeRF class uses several randomly built reegression trees for prediction. It randomly selects sub-samples of 'bRatio * x.dim' size from the data x and y to build nTrees regression trees. The predict method uses the average over all trees. Note: By default this class does not select sub-features to build the trees (like Bagging Trees) Set use_fb (feature bagging) to true to turn this capability on

Value parameters

fname_

the names of the variables/features (defaults to null => auto-generate))

hparam

the hyper-parameters to the random forest (defaults to RegressionTree.hp)

use_fb

whether to use feature bagging (select subsets of the features)

x

the input/data matrix (instances by features)

y

the ouput/response vector (instances)

Attributes

Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
class RegressionWLS(x: MatrixD, y: VectorD, fname_: Array[String], var w: VectorD, hparam: HyperParameter) extends Regression

The RegressionWLS class supports weighted multiple linear regression. In this case, x is multi-dimensional [1, x_1, ... x_k]. Weights are set to the inverse of a variable's variance, so they can compensate for such variability (heteroscedasticity). Fit the parameter vector b in the regression equation yy = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e where e represents the residuals (the part not explained by the model). Use Weighted Least-Squares (minimizing the residuals) to fit the parameter vector b = fac.solve (.) The data matrix x is reweighted x = rootW * x and the response vector yy is reweighted y = rootW * yy where rootW is the square root of the weights.

The RegressionWLS class supports weighted multiple linear regression. In this case, x is multi-dimensional [1, x_1, ... x_k]. Weights are set to the inverse of a variable's variance, so they can compensate for such variability (heteroscedasticity). Fit the parameter vector b in the regression equation yy = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e where e represents the residuals (the part not explained by the model). Use Weighted Least-Squares (minimizing the residuals) to fit the parameter vector b = fac.solve (.) The data matrix x is reweighted x = rootW * x and the response vector yy is reweighted y = rootW * yy where rootW is the square root of the weights.

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (defaults to Regression.hp)

w

the weight vector (if null, compute in companion object)

x

the data/input m-by-n matrix (augment with a first column of ones to include intercept in model)

y

the response/output m vector

Attributes

See also

en.wikipedia.org/wiki/Least_squares#Weighted_least_squares These are then passed to Ordinary Least Squares (OLS) Regression. Five factorization techniques are provided: 'QR' // QR Factorization: slower, more stable (default) 'Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'SVD' // Singular Value Decomposition: slowest, most robust 'LU' // LU Factorization: better than Inverse 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique

Companion
object
Supertypes
class Regression
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object RegressionWLS

The RegressionWLS companion object provides methods for setting weights and testing.

The RegressionWLS companion object provides methods for setting weights and testing.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class RidgeRegression(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter) extends Predictor, Fit

The RidgeRegression class supports multiple linear ridge regression. In this case, x is multi-dimensional [x_1, ... x_k]. Ridge regression puts a penalty on the L2 norm of the parameters b to reduce the chance of them taking on large values that may lead to less robust models. Both the input matrix x and the response vector y are centered (zero mean). Fit the parameter vector b in the regression equation y = b dot x + e = b_1 * x_1 + ... b_k * x_k + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve for the parameter vector b using the regularized Normal Equations: b = fac.solve (.) with regularization x.t * x + λ * I Five factorization techniques are provided: 'QR' // QR Factorization: slower, more stable (default) 'Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'SVD' // Singular Value Decomposition: slowest, most robust 'LU' // LU Factorization: similar, but better than inverse 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique

The RidgeRegression class supports multiple linear ridge regression. In this case, x is multi-dimensional [x_1, ... x_k]. Ridge regression puts a penalty on the L2 norm of the parameters b to reduce the chance of them taking on large values that may lead to less robust models. Both the input matrix x and the response vector y are centered (zero mean). Fit the parameter vector b in the regression equation y = b dot x + e = b_1 * x_1 + ... b_k * x_k + e where e represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve for the parameter vector b using the regularized Normal Equations: b = fac.solve (.) with regularization x.t * x + λ * I Five factorization techniques are provided: 'QR' // QR Factorization: slower, more stable (default) 'Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'SVD' // Singular Value Decomposition: slowest, most robust 'LU' // LU Factorization: similar, but better than inverse 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the shrinkage hyper-parameter, lambda (0 => OLS) in the penalty term 'lambda * b dot b'

x

the centered data/input m-by-n matrix NOT augmented with a first column of ones

y

the centered response/output m-vector

Attributes

See also

statweb.stanford.edu/~tibs/ElemStatLearn/

Companion
object
Supertypes
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object RidgeRegression

The RidgeRegression companion object defines hyper-parameters and provides factory methods creating ridge regression models.

The RidgeRegression companion object defines hyper-parameters and provides factory methods creating ridge regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class RoundRegression(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter) extends Regression

The RoundRegression class supports rounded multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the transformed regression equation y = round (b dot x) + e = round (b_0 + b_1 * x_1 + b_2 * x_2 ... b_k * x_k) + e where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector 'b'

The RoundRegression class supports rounded multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the transformed regression equation y = round (b dot x) + e = round (b_0 + b_1 * x_1 + b_2 * x_2 ... b_k * x_k) + e where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector 'b'

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (defaults to Regression.hp)

x

the data/input matrix

y

the response/output vector

Attributes

Companion
object
Supertypes
class Regression
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object RoundRegression

The RoundRegression companion object provides factory methods for creating rounded regression models.

The RoundRegression companion object provides factory methods for creating rounded regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
trait Scaling

The Scaling trait supports rescaling of data values. When the scale flag is on/true, the companion object factory apply/rescale functions should rescale or normalize the data appropriately to the particular modeling technique (or even to the level of the activation function used).

The Scaling trait supports rescaling of data values. When the scale flag is on/true, the companion object factory apply/rescale functions should rescale or normalize the data appropriately to the particular modeling technique (or even to the level of the activation function used).

Attributes

See also

ActivationFun. In ScalaTion, model constructors do not rescale, but apply/rescale functions that call model constructors need to provide this option.

Supertypes
class Object
trait Matchable
class Any
Known subtypes
object ELM_3L1
object NeuralNet_2L
object NeuralNet_3L
object NeuralNet_XL
object NeuralNet_XLT
object Perceptron
Show all
enum SelectionTech

The SelectionTech enumeration indicates the available feature selection techniques.

The SelectionTech enumeration indicates the available feature selection techniques.

Attributes

Supertypes
trait Enum
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
class SimpleExpRegression(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter, nonneg: Boolean) extends Predictor, Fit, NoSubModels

The SimpleExpRegression class supports exponential regression. In this case, x is [1, x_1]. Fit the parameter vector b in the exponential regression equation log (mu (x)) = b dot x = b_0 + b_1 * x_1

The SimpleExpRegression class supports exponential regression. In this case, x is [1, x_1]. Fit the parameter vector b in the exponential regression equation log (mu (x)) = b dot x = b_0 + b_1 * x_1

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (currently none)

nonneg

whether to check that responses are nonnegative (defaults to true)

x

the data/input matrix

y

the response/output vector

Attributes

See also
Companion
object
Supertypes
trait NoSubModels
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object SimpleExpRegression

The SimpleExpRegression companion object provides factory methods for creating simple exponential regression models.

The SimpleExpRegression companion object provides factory methods for creating simple exponential regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class SimpleRegression(x: MatrixD, y: VectorD, fname_: Array[String]) extends Predictor, Fit, NoSubModels

The SimpleRegression class supports simple linear regression. In this case, the vector x consists of the constant one and a single variable x1, i.e., (1, x1). Fit the parameter vector 'b' in the regression equation y = b dot x + e = [b0, b1] dot [1, x1] + e = b0 + b1 * x1 + e where e represents the residuals (the part not explained by the model).

The SimpleRegression class supports simple linear regression. In this case, the vector x consists of the constant one and a single variable x1, i.e., (1, x1). Fit the parameter vector 'b' in the regression equation y = b dot x + e = [b0, b1] dot [1, x1] + e = b0 + b1 * x1 + e where e represents the residuals (the part not explained by the model).

Value parameters

fname_

the feature/variable names (only use the first two names)(defaults to null)

x

the data/input matrix augmented with a first column of ones (only use the first two columns [1, x1])

y

the response/output vector

Attributes

Companion
object
Supertypes
trait NoSubModels
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object SimpleRegression

The SimpleRegression companion object provides a simple factory method for building simple regression linear regression models.

The SimpleRegression companion object provides a simple factory method for building simple regression linear regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class SimplerRegression(x: MatrixD, y: VectorD, fname_: Array[String]) extends Predictor, Fit, NoSubModels

The SimplerRegression class supports simpler linear regression. In this case, the vector x consists of a single variable x0. Fit the parameter vector b in the regression equation y = b dot x + e = [b0] dot [x0] + e = b0 * x0 + e where 'e' represents the residuals (the part not explained by the model). The simpler regression model has no intercept parameter, only a slope parameter.

The SimplerRegression class supports simpler linear regression. In this case, the vector x consists of a single variable x0. Fit the parameter vector b in the regression equation y = b dot x + e = [b0] dot [x0] + e = b0 * x0 + e where 'e' represents the residuals (the part not explained by the model). The simpler regression model has no intercept parameter, only a slope parameter.

Value parameters

fname_

the feature/variable names (only use the first name)(defaults to null)

x

the data/input matrix (only use the first column)

y

the response/output vector

Attributes

See also

SimpleRegression for both intercept and slope parameters

Companion
object
Supertypes
trait NoSubModels
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object SimplerRegression

The SimplerRegression companion object provides a simple factory method for building simple regression linear regression models.

The SimplerRegression companion object provides a simple factory method for building simple regression linear regression models.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class SumQueue(q: Int)

The SumQueue class retains the last q elements as well as the running total in sum and number of elements in size_, making it efficient to compute moving averages.

The SumQueue class retains the last q elements as well as the running total in sum and number of elements in size_, making it efficient to compute moving averages.

Value parameters

q

the number of elements to retain in the queue

Attributes

Supertypes
class Object
trait Matchable
class Any
class SumSqQueue(q: Int)

The SumQueue class retains the last q elements as well as the running total in sum and number of elements in size_, making it efficient to compute moving averages.

The SumQueue class retains the last q elements as well as the running total in sum and number of elements in size_, making it efficient to compute moving averages.

Value parameters

q

the number of elements to retain in the queue

Attributes

Supertypes
class Object
trait Matchable
class Any
object SymLassoRegression

The SymLassoRegression object supports symbolic ridge regression that allows variables/columns to be raised to various powers, e.g., x^2, x^3, x^.5. Note, x~^p is a column-wise power function (each column raised to p-th power). IMPORTANT: must not include INTERCEPT (column of ones) in initial data matrix), i.e., DO NOT include a column of ones in x (will cause singularity in expanded matrix). Method signatures are the as same as for SymbolicRegression, except there is NO intercept ARGUMENT.

The SymLassoRegression object supports symbolic ridge regression that allows variables/columns to be raised to various powers, e.g., x^2, x^3, x^.5. Note, x~^p is a column-wise power function (each column raised to p-th power). IMPORTANT: must not include INTERCEPT (column of ones) in initial data matrix), i.e., DO NOT include a column of ones in x (will cause singularity in expanded matrix). Method signatures are the as same as for SymbolicRegression, except there is NO intercept ARGUMENT.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
object SymRidgeRegression

The SymRidgeRegression object supports symbolic ridge regression that allows variables/columns to be raised to various powers, e.g., x^2, x^3, x^.5. Note, x~^p is a column-wise power function (each column raised to p-th power). IMPORTANT: must not include INTERCEPT (column of ones) in initial data matrix), i.e., DO NOT include a column of ones in x (will cause singularity in expanded matrix). Method signatures are the as same as for SymbolicRegression, except there is NO intercept ARGUMENT.

The SymRidgeRegression object supports symbolic ridge regression that allows variables/columns to be raised to various powers, e.g., x^2, x^3, x^.5. Note, x~^p is a column-wise power function (each column raised to p-th power). IMPORTANT: must not include INTERCEPT (column of ones) in initial data matrix), i.e., DO NOT include a column of ones in x (will cause singularity in expanded matrix). Method signatures are the as same as for SymbolicRegression, except there is NO intercept ARGUMENT.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
object SymbolicRegression

The SymbolicRegression object supports symbolic regression that allows variables/columns to be raised to various powers, e.g., x^2, x^3, x^.5. Note, x~^p is a column-wise power function (each column raised to p-th power). IMPORTANT: must not include intercept (column of ones) in initial data matrix), i.e., DO NOT include a column of ones in x (will cause singularity in expanded matrix).

The SymbolicRegression object supports symbolic regression that allows variables/columns to be raised to various powers, e.g., x^2, x^3, x^.5. Note, x~^p is a column-wise power function (each column raised to p-th power). IMPORTANT: must not include intercept (column of ones) in initial data matrix), i.e., DO NOT include a column of ones in x (will cause singularity in expanded matrix).

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
class TestFit(m: Int) extends Fit

The TestFit class can be used for comparing two vectors on the basis of QoF. The degrees of freedom (dfm) for the "model" is assumed to be 1. Can be used when the degrees of freedom are not known.

The TestFit class can be used for comparing two vectors on the basis of QoF. The degrees of freedom (dfm) for the "model" is assumed to be 1. Can be used when the degrees of freedom are not known.

Value parameters

m

the size of vectors to compare

Attributes

Supertypes
trait Fit
trait FitM
class Object
trait Matchable
class Any
class TranRegression(x: MatrixD, y: VectorD, fname_: Array[String], hparam: HyperParameter, tran: FunctionS2S, itran: FunctionS2S) extends Regression

The TranRegression class supports transformed multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the transformed regression equation transform (y) = b dot x + e = b_0 + b_1 * x_1 + b_2 * x_2 ... b_k * x_k + e where 'e' represents the residuals (the part not explained by the model) and 'transform' is the function (defaults to log) used to transform the response vector 'y'. Common transforms include 'log (y)', 'sqrt (y)' when 'y > 0', or even 'sq (y)', 'exp (y)'. More generally, a Box-Cox Transformation may be applied.

The TranRegression class supports transformed multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the transformed regression equation transform (y) = b dot x + e = b_0 + b_1 * x_1 + b_2 * x_2 ... b_k * x_k + e where 'e' represents the residuals (the part not explained by the model) and 'transform' is the function (defaults to log) used to transform the response vector 'y'. Common transforms include 'log (y)', 'sqrt (y)' when 'y > 0', or even 'sq (y)', 'exp (y)'. More generally, a Box-Cox Transformation may be applied.

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (defaults to Regression.hp)

itran

the inverse transformation function to rescale predictions to original y scale (defaults to exp)

tran

the transformation function (defaults to log)

x

the data/input m-by-n matrix

y

the response/output m-vector

Attributes

See also

citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.469.7176&rep=rep1&type=pdf Use Least-Squares (minimizing the residuals) to fit the parameter vector 'b' Note: this class does not provide transformations on columns of matrix 'x'.

Companion
object
Supertypes
class Regression
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object TranRegression

The TranRegression companion object provides transformation and inverse transformation function based on the parameter 'lambda'. It support the family of Box-Cox transformations.

The TranRegression companion object provides transformation and inverse transformation function based on the parameter 'lambda'. It support the family of Box-Cox transformations.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
object TranRegressionEx

The TranRegressionEx provides a sample dataset for testing purposes. Move the comments on the line used to generate the response y(k) to test 1D and 2D cases.

The TranRegressionEx provides a sample dataset for testing purposes. Move the comments on the line used to generate the response y(k) to test 1D and 2D cases.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
class TrigRegression(t: MatrixD, y: VectorD, ord: Int, fname_: Array[String], hparam: HyperParameter) extends Regression

The TrigRegression class supports trigonometric regression. In this case, 't' is expanded to '[1, sin (wt), cos (wt), sin (2wt), cos (2wt), ...]'. Fit the parameter vector 'b' in the regression equation y = b dot x + e = b_0 + b_1 sin (wt) + b_2 cos (wt) + b_3 sin (2wt) + b_4 cos (2wt) + ... + e where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve for the parameter vector 'b' using the Normal Equations: x.t * x * b = x.t * y b = fac.solve (.)

The TrigRegression class supports trigonometric regression. In this case, 't' is expanded to '[1, sin (wt), cos (wt), sin (2wt), cos (2wt), ...]'. Fit the parameter vector 'b' in the regression equation y = b dot x + e = b_0 + b_1 sin (wt) + b_2 cos (wt) + b_3 sin (2wt) + b_4 cos (2wt) + ... + e where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to solve for the parameter vector 'b' using the Normal Equations: x.t * x * b = x.t * y b = fac.solve (.)

Value parameters

fname_

the feature/variable names (defaults to null)

hparam

the hyper-parameters (defaults to Regression.hp)

ord

the order (k), maximum multiplier in the trig function (kwt)

t

the initial data/input m-by-1 matrix: t_i expands to x_i

y

the response/ouput vector

Attributes

See also

link.springer.com/article/10.1023%2FA%3A1022436007242#page-1

Companion
object
Supertypes
class Regression
trait Fit
trait FitM
trait Predictor
trait Model
class Object
trait Matchable
class Any
Show all
object TrigRegression

The TrigRegression companion object provides factory methods and functions for creating functional forms.

The TrigRegression companion object provides factory methods and functions for creating functional forms.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
case class Variable(xj: VectorD, j: Int, kind: VariableKind, name_: String, concept: String)

Several modeling techniques such as decision trees need to divide the values into groups, e.g., for branch values: When 'xj' is categorical, these will be all its distinct values. Otherwise, these will be 0 (up to threshold) or 1 (above threshold).

The Variable class provides meta-data for a variable including its kind, distinct values, name and optional ontological concept. The variable may be an input variable (feature) or an output variable (response). Typically, it represents a column 'xj' in a data matrix.

Several modeling techniques such as decision trees need to divide the values into groups, e.g., for branch values: When 'xj' is categorical, these will be all its distinct values. Otherwise, these will be 0 (up to threshold) or 1 (above threshold).

Value parameters

concept

an optional URI for an optological concept

j

the index position within the relevant data matrix

kind

indication of the variable kind

name

the name of column (feature or response)

xj

the column vector (feature/response)

Attributes

See also

classifier.Node for 'threshold'

Companion
object
Supertypes
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
object Variable

The Variable companion object provides utilities for variables.

The Variable companion object provides utilities for variables.

Attributes

Companion
class
Supertypes
trait Product
trait Mirror
class Object
trait Matchable
class Any
Self type
Variable.type
enum VariableKind

The VariableKind enumeration indicates the kind of variable.

The VariableKind enumeration indicates the kind of variable.

Attributes

Supertypes
trait Enum
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
final class activationFunTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class activationFunTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class activationFunTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class activationFunTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class activationFunTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class example_AutoMPG_Correlation

Attributes

Supertypes
class Object
trait Matchable
class Any
final class example_AutoMPG_NullModel

Attributes

Supertypes
class Object
trait Matchable
class Any
final class example_AutoMPG_QuadRegression

Attributes

Supertypes
class Object
trait Matchable
class Any
final class example_AutoMPG_Regression

Attributes

Supertypes
class Object
trait Matchable
class Any
final class example_AutoMPG_SimpleRegression

Attributes

Supertypes
class Object
trait Matchable
class Any
final class example_AutoMPG_SimplerRegression

Attributes

Supertypes
class Object
trait Matchable
class Any
final class example_BPressureTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class example_BPressureTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class example_BasketBallTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class expRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class expRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fitITest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fitTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class imputationTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class imputationTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class kNN_RegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class kNN_RegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class kNN_RegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class lassoRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class lassoRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class lassoRegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixTransformTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixTransformTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class nonlinearRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class nullModelTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class nullModelTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class outlierTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class outlierTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class outlierTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class perceptronTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class perceptronTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class perceptronTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class perceptronTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class perceptronTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class poissonRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class poissonRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class polyORegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class polyORegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class polyRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class polyRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class predictorTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionCatTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionCatTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionCatTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionCatTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionCatTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTest7

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeGBTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeGBTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeGBTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeGBTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeGBTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeGBTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeMTTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeMTTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeMTTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeRFTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeRFTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeRFTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeRFTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionTreeTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionWLSTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class regressionWLSTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class ridgeRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class ridgeRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class ridgeRegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class ridgeRegressionTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class ridgeRegressionTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class ridgeRegressionTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class roundRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleExpRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleExpRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleExpRegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleRegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleRegressionTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleRegressionTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleRegressionTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleRegressionTest7

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simpleRegressionTest8

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simplerRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simplerRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simplerRegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class simplerRegressionTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class sumQueueTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class sumQueueTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symLassoRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symLassoRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symLassoRegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symLassoRegressionTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symLassoRegressionTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symLassoRegressionTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symLassoRegressionTest7

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symLassoRegressionTest8

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symLassoRegressionTest9

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symRidgeRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symRidgeRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symRidgeRegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symRidgeRegressionTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symRidgeRegressionTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symRidgeRegressionTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symRidgeRegressionTest7

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symRidgeRegressionTest8

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symRidgeRegressionTest9

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symbolicRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symbolicRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symbolicRegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symbolicRegressionTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symbolicRegressionTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symbolicRegressionTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symbolicRegressionTest7

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symbolicRegressionTest8

Attributes

Supertypes
class Object
trait Matchable
class Any
final class symbolicRegressionTest9

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tranRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tranRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tranRegressionTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tranRegressionTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tranRegressionTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tranRegressionTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tranRegressionTest7

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tranRegressionTest8

Attributes

Supertypes
class Object
trait Matchable
class Any
final class trigRegressionTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class trigRegressionTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class variableTest

Attributes

Supertypes
class Object
trait Matchable
class Any

Types

type FunctionP2S = (VectorD, VectorD) => Double

Function type for f(x, b) that maps a pair of vectors to a double

Function type for f(x, b) that maps a pair of vectors to a double

Attributes

type MatrixI = MatrixD
type Xj2p = (Int, Double)

Value members

Concrete methods

def activationFunTest(): Unit

The activationFunTest main function tests the ActivationFun object. This test individually plots the activation function f(t).

The activationFunTest main function tests the ActivationFun object. This test individually plots the activation function f(t).

runMain scalation.modeling.activationFunTest

Attributes

def activationFunTest2(): Unit

The activationFunTest2 main function tests the ActivationFun object. This test plots similar pairs of activation functions f(t).

The activationFunTest2 main function tests the ActivationFun object. This test plots similar pairs of activation functions f(t).

runMain scalation.modeling.activationFunTest2

Attributes

def activationFunTest3(): Unit

The activationFunTest3 main function tests the ActivationFun object. This test plots the derivatives of the activation functions f'(t).

The activationFunTest3 main function tests the ActivationFun object. This test plots the derivatives of the activation functions f'(t).

runMain scalation.modeling.activationFunTest2

Attributes

def activationFunTest4(): Unit

The activationFunTest4 main function tests the ActivationFun object.

The activationFunTest4 main function tests the ActivationFun object.

Attributes

See also

en.wikipedia.org/wiki/Softmax_function

runMain scalation.modeling.activationFunTest4

def activationFunTest5(): Unit

The activationFunTest3 main function tests the ActivationFun object.

The activationFunTest3 main function tests the ActivationFun object.

runMain scalation.modeling.activationFunTest5

Attributes

def center(x: MatrixD, mu_x: VectorD): MatrixD

Center matrix x to zero mean, column-wise, by subtracting the mean.

Center matrix x to zero mean, column-wise, by subtracting the mean.

Value parameters

mu_x

the vector of column means of matrix x

x

the matrix to center

Attributes

def denormalize(mu_sig: (VectorD, VectorD))(x_n: MatrixD): MatrixD

Denormalize the matrix x_n from zero mean and unit standard deviation, column-wise, by multiplying by the standard deviation and adding the mean. Don't denormalize if the standard deviation is nearly zero.

Denormalize the matrix x_n from zero mean and unit standard deviation, column-wise, by multiplying by the standard deviation and adding the mean. Don't denormalize if the standard deviation is nearly zero.

Value parameters

mu_sig

the mean and standard deviation vectors of original matrix x where mu_x the vector of column means of matrix x sig_x the vector of column standard deviations of matrix x

x_n

the matrix to denormalize

Attributes

def denormalizeV(mu_sig: (Double, Double))(x_n: VectorD): VectorD

Denormalize the vector x_n from zero mean and unit standard deviation, by multiplying by the standard deviation and adding the mean. Don't denormalize if the standard deviation is nearly zero.

Denormalize the vector x_n from zero mean and unit standard deviation, by multiplying by the standard deviation and adding the mean. Don't denormalize if the standard deviation is nearly zero.

Value parameters

mu_sig

the column vector's mean and standard deviation

x_n

the vector to denormalize

Attributes

def example_AutoMPG_Correlation(): Unit

The example_AutoMPG_Correlation main function performs correlation analysis on the UCI AutoMPG dataset.

The example_AutoMPG_Correlation main function performs correlation analysis on the UCI AutoMPG dataset.

Attributes

See also

archive.ics.uci.edu/ml/datasets/Auto+MPG

runMain scalation.modeling.example_AutoMPG_Correlation

def example_AutoMPG_NullModel(): Unit

The example_AutoMPG_NullModel main function performs NullModel on the UCI AutoMPG dataset.

The example_AutoMPG_NullModel main function performs NullModel on the UCI AutoMPG dataset.

Attributes

See also

archive.ics.uci.edu/ml/datasets/Auto+MPG

runMain scalation.modeling.example_AutoMPG_NullModel

def example_AutoMPG_QuadRegression(): Unit

The example_AutoMPG_QuadRegression main function performs quadratic on the UCI AutoMPG dataset.

The example_AutoMPG_QuadRegression main function performs quadratic on the UCI AutoMPG dataset.

Attributes

See also

archive.ics.uci.edu/ml/datasets/Auto+MPG

runMain scalation.modeling.example_AutoMPG_QuadRegression

def example_AutoMPG_Regression(): Unit

The example_AutoMPG_Regression main function performs Regression on the UCI AutoMPG dataset.

The example_AutoMPG_Regression main function performs Regression on the UCI AutoMPG dataset.

Attributes

See also

archive.ics.uci.edu/ml/datasets/Auto+MPG

runMain scalation.modeling.example_AutoMPG_Regression

def example_AutoMPG_SimpleRegression(): Unit

The example_AutoMPG_SimpleRegression main function performs SimpleRegression on the UCI AutoMPG dataset.

The example_AutoMPG_SimpleRegression main function performs SimpleRegression on the UCI AutoMPG dataset.

Attributes

See also

archive.ics.uci.edu/ml/datasets/Auto+MPG

runMain scalation.modeling.example_AutoMPG_SimpleRegression

def example_AutoMPG_SimplerRegression(): Unit

The example_AutoMPG_SimplerRegression main function performs SimplerRegression on the UCI AutoMPG dataset.

The example_AutoMPG_SimplerRegression main function performs SimplerRegression on the UCI AutoMPG dataset.

Attributes

See also

archive.ics.uci.edu/ml/datasets/Auto+MPG

runMain scalation.modeling.example_AutoMPG_SimplerRegression

def example_BPressureTest(): Unit

The example_BPressureTest main function tests the Example_BPressure by printing out of the vectors and matrices.

The example_BPressureTest main function tests the Example_BPressure by printing out of the vectors and matrices.

runMain scalation.modeling.example_BPressureTest

Attributes

def example_BPressureTest2(): Unit

The example_BPressureTest2 main function tests the multi-collinearity method in the Regression class using the following regression equation. y = b dot x = b_1x_1 + b_2x_2 + b_3*x_3 + b_4 * x_4

The example_BPressureTest2 main function tests the multi-collinearity method in the Regression class using the following regression equation. y = b dot x = b_1x_1 + b_2x_2 + b_3*x_3 + b_4 * x_4

Attributes

See also

online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html

online.stat.psu.edu/online/development/stat501/data/bloodpress.txt

runMain scalation.modeling.example_BPressureTest2

def example_BasketBallTest(): Unit

The example_BasketBallTest main function tests the Regression class using the Basketball dataset.

The example_BasketBallTest main function tests the Regression class using the Basketball dataset.

runMain scalation.modeling.example_BasketBallTest

Attributes

def expRegressionTest: Unit

The expRegressionTest main function tests ExpRegression class using the following exponential regression problem.

The expRegressionTest main function tests ExpRegression class using the following exponential regression problem.

runMain scalation.modeling.expRegressionTest

Attributes

def expRegressionTest2(): Unit

The expRegressionTest2 main function has a basic test for the ExpRegression class.

The expRegressionTest2 main function has a basic test for the ExpRegression class.

runMain scalation.modeling.expRegressionTest

Attributes

inline def extreme(x: VectorD): (Double, Double)

Return the extreme values (min, max) for vector x.

Return the extreme values (min, max) for vector x.

Value parameters

x

the vector whose extreme values are sought

Attributes

def extreme(x: MatrixD): (VectorD, VectorD)

Return the extreme values (min, max) for matrix x, for each column.

Return the extreme values (min, max) for matrix x, for each column.

Value parameters

x

the matrix whose extreme values are sought

Attributes

def featureSubSample(x: MatrixD, nFeat: Int, stream: Int): (MatrixD, Set[Int])

Create a random sub-sample of features from matrix x, returning the sub-sample matrix along with the indices selected (as a set).

Create a random sub-sample of features from matrix x, returning the sub-sample matrix along with the indices selected (as a set).

Value parameters

nFeat

the desired number of features in the sub-sample

stream

the random number stream to use

x

the original input/data matrix

Attributes

def fitITest(): Unit

The fitITest main function is used to test the FitI class on a simulated time series.

The fitITest main function is used to test the FitI class on a simulated time series.

Attributes

See also

scalation.modeling.forecasting.randomWalkTest3 for another test case

runMain scalation.modeling.fitITest

def fitTest(): Unit

The fitTest main function is used to test the Fit trait on a simulated dataset.

The fitTest main function is used to test the Fit trait on a simulated dataset.

runMain scalation.modeling.fitTest

Attributes

def imputationTest(): Unit

The imputationTest main function is used to test the objects extending the Imputation trait.

The imputationTest main function is used to test the objects extending the Imputation trait.

runMain scalation.modeling.imputationTest

Attributes

def imputationTest2(): Unit

The imputationTest2 main function is used to test the objects extending the Imputation trait.

The imputationTest2 main function is used to test the objects extending the Imputation trait.

runMain scalation.modeling.imputationTest2

Attributes

def kNN_RegressionTest(): Unit

The kNN_RegressionTest main function is used to test the KNN_Regression class.

The kNN_RegressionTest main function is used to test the KNN_Regression class.

runMain scalation.modeling.kNN_RegressionTest

Attributes

def kNN_RegressionTest2(): Unit

The kNN_RegressionTest2 main function is used to test the KNN_Regression class.

The kNN_RegressionTest2 main function is used to test the KNN_Regression class.

runMain scalation.modeling.kNN_RegressionTest2

Attributes

def kNN_RegressionTest3(): Unit

The kNN_RegressionTest3 main function is used to test the KNN_predictor class.

The kNN_RegressionTest3 main function is used to test the KNN_predictor class.

runMain scalation.modeling.kNN_RegressionTest3

Attributes

def lassoRegressionTest(): Unit

The lassoRegressionTest main function tests LassoRegression class using the following regression equation. y = b dot x = b_0 + b_1x_1 + b_2x_2. It comapres LassoRegression to Regression.

The lassoRegressionTest main function tests LassoRegression class using the following regression equation. y = b dot x = b_0 + b_1x_1 + b_2x_2. It comapres LassoRegression to Regression.

Attributes

See also

http://statmaster.sdu.dk/courses/st111/module03/index.html

runMain scalation.modeling.lassoRegressionTest

def lassoRegressionTest2(): Unit

The lassoRegressionTest2 main function tests LassoRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2. Try non-default value for the 'lambda' hyper-parameter.

The lassoRegressionTest2 main function tests LassoRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2. Try non-default value for the 'lambda' hyper-parameter.

runMain scalation.modeling.lassoRegressionTest2

Attributes

def lassoRegressionTest3(): Unit

The lassoRegressionTest3 main function tests LassoRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2. Test regression, forward selection and backward elimination.

The lassoRegressionTest3 main function tests LassoRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2. Test regression, forward selection and backward elimination.

runMain scalation.modeling.lassoRegressionTest3

Attributes

def matrixTransformTest(): Unit

The matrixTransformTest main function is used to test the MatrixTransform object. It tests centering, scaling and normalization.

The matrixTransformTest main function is used to test the MatrixTransform object. It tests centering, scaling and normalization.

runMain scalation.modeling.matrixTransformTest

Attributes

def matrixTransformTest2(): Unit

The matrixTransformTest2 main function is used to test the MatrixTransform object. It tests usage of tran and itran functional variables.

The matrixTransformTest2 main function is used to test the MatrixTransform object. It tests usage of tran and itran functional variables.

runMain scalation.modeling.matrixTransformTest2

Attributes

inline def mean_stdev(x: VectorD): (Double, Double)

Return the mean and standard deviation stats for vector x

Return the mean and standard deviation stats for vector x

Value parameters

x

the vector whose stats are sought

Attributes

def nonlinearRegressionTest(): Unit

The nonlinearRegressionTest object tests the NonlinearRegression class: y = f(x; b) = b0 + exp (b1 * x0).

The nonlinearRegressionTest object tests the NonlinearRegression class: y = f(x; b) = b0 + exp (b1 * x0).

Attributes

See also

www.bsos.umd.edu/socy/alan/stats/socy602_handouts/kut86916_ch13.pdf Answers: sse = 49.45929986243339 fit = (VectorD (58.606566327280426, -0.03958645286504356), 0.9874574894685292) predict (VectorD (50.0)) = 8.09724678182599 FIX: check this example

runMain scalation.modeling.nonlinearRegressionTest

def normalize(mu_sig: (VectorD, VectorD))(x: MatrixD): MatrixD

Normalize the matrix x to zero mean and unit standard deviation, column-wise, by subtracting the mean and dividing by the standard deviation. Don't normalize if the standard deviation is nearly zero.

Normalize the matrix x to zero mean and unit standard deviation, column-wise, by subtracting the mean and dividing by the standard deviation. Don't normalize if the standard deviation is nearly zero.

Value parameters

mu_sig

the mean and standard deviation vectors of original matrix x where mu_x the vector of column means of matrix x sig_x the vector of column standard deviations of matrix x

x

the matrix to normalize

Attributes

def normalizeV(mu_sig: (Double, Double))(x: VectorD): VectorD

Normalize the vector x to zero mean and unit standard deviation, by subtracting the mean and dividing by the standard deviation. Don't normalize if the standard deviation is nearly zero.

Normalize the vector x to zero mean and unit standard deviation, by subtracting the mean and dividing by the standard deviation. Don't normalize if the standard deviation is nearly zero.

Value parameters

mu_sig

the column vector's mean and standard deviation

x

the vector to normalize

Attributes

def nullModelTest(): Unit

The nullModelTest main function is used to test the NullModel class. y = b dot x + e = b0 + e

The nullModelTest main function is used to test the NullModel class. y = b dot x + e = b0 + e

runMain scalation.modeling.nullModelTest

Attributes

def nullModelTest2(): Unit

The nullModelTest2 main function is used to test the NullModel class. y = b dot x + e = b0 + e

The nullModelTest2 main function is used to test the NullModel class. y = b dot x + e = b0 + e

runMain scalation.modeling.nullModelTest2

Attributes

def orderByY(y_: VectorD, yp_: VectorD): (VectorD, VectorD)

Order vectors y_ and yp_ according to the ascending order of y_. This can be used for graphical comparison or true and predicted values.

Order vectors y_ and yp_ according to the ascending order of y_. This can be used for graphical comparison or true and predicted values.

Value parameters

y_

the vector to order by (e.g., true response values)

yp_

the vector to be order by y_ (e.g., predicted response values)

Attributes

def orderByYY(y_: MatrixD, yp_: MatrixD): (MatrixD, MatrixD)

Order matrices y_ and yp_ according to the ascending order of y_ (column vector by column vector). This can be used for graphical comparison or true and predicted values.

Order matrices y_ and yp_ according to the ascending order of y_ (column vector by column vector). This can be used for graphical comparison or true and predicted values.

Value parameters

y_

the matrix to order by (e.g., true response values)

yp_

the matrix to be order by y_ (e.g., predicted response values)

Attributes

def outlierTest(): Unit

The outlierTest main function is used to test the Outliers Detection techniques presented in the Outliers trait for a vector of doubles.

The outlierTest main function is used to test the Outliers Detection techniques presented in the Outliers trait for a vector of doubles.

runMain scalation.modeling.outlierTest

Attributes

def outlierTest2(): Unit

The outlierTest2 main function is used to test the Outliers Detection techniques presented in the Outliers trait for a matrix and vector doubles.

The outlierTest2 main function is used to test the Outliers Detection techniques presented in the Outliers trait for a matrix and vector doubles.

runMain scalation.modeling.outlierTest2

Attributes

def outlierTest3(): Unit

The outlierTest3 main function is used to test the Outliers Detection techniques presented in the Outliers trait for a matrix and vector doubles.

The outlierTest3 main function is used to test the Outliers Detection techniques presented in the Outliers trait for a matrix and vector doubles.

runMain scalation.modeling.outlierTest3

Attributes

def perceptronTest(): Unit

The perceptronTest object trains a perceptron on a small dataset with variables x1 and x2. The model equation is the following: y = sigmoid (b dot x) = sigmoid (b0 + b1x1 + b2x2) Does not call the train method; improvements steps for sigmoid are explicitly in code below.

The perceptronTest object trains a perceptron on a small dataset with variables x1 and x2. The model equation is the following: y = sigmoid (b dot x) = sigmoid (b0 + b1x1 + b2x2) Does not call the train method; improvements steps for sigmoid are explicitly in code below.

runMain scalation.modeling.perceptronTest

Attributes

def perceptronTest2(): Unit

The perceptronTest2 object trains a perceptron on a small dataset of temperatures from counties in Texas where the variables/factors to consider are Latitude (x1), Elevation (x2) and Longitude (x3). The model equation is the following: y = sigmoid (w dot x) = sigmoid (w0 + w1x1 + w2x2 + w3*x3) This test case illustrates how to transform the columns of the matrix so that the sigmoid activation function can work effectively.

The perceptronTest2 object trains a perceptron on a small dataset of temperatures from counties in Texas where the variables/factors to consider are Latitude (x1), Elevation (x2) and Longitude (x3). The model equation is the following: y = sigmoid (w dot x) = sigmoid (w0 + w1x1 + w2x2 + w3*x3) This test case illustrates how to transform the columns of the matrix so that the sigmoid activation function can work effectively.

runMain scalation.modeling.perceptronTest2

Attributes

def perceptronTest3(): Unit

The perceptronTest3 main function tests the Perceptron class using the AutoMPG dataset. It test cross validation.

The perceptronTest3 main function tests the Perceptron class using the AutoMPG dataset. It test cross validation.

runMain scalation.modeling.perceptronTest3

Attributes

def perceptronTest4(): Unit

The perceptronTest4 main function tests the Perceptron class using the AutoMPG dataset. Assumes no missing values. It tests forward selection.

The perceptronTest4 main function tests the Perceptron class using the AutoMPG dataset. Assumes no missing values. It tests forward selection.

runMain scalation.modeling.perceptronTest4

Attributes

def perceptronTest5(): Unit

The perceptronTest5 main function tests the Perceptron class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

The perceptronTest5 main function tests the Perceptron class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

runMain scalation.modeling.perceptronTest5

Attributes

def poissonRegressionTest(): Unit

The poissonRegressionTest main function tests the PoissonRegression class.

The poissonRegressionTest main function tests the PoissonRegression class.

Attributes

See also

http://www.cookbook-r.com/Statistical_analysis/Logistic_regression/ Answer: b = (-8.8331, 0.4304), n_dev = 43.860, r_dev = 25.533, aci = 29.533, pseudo_rSq = 0.4178

runMain scalation.modeling.poissonRegressionTest

def poissonRegressionTest2(): Unit

The poissonRegressionTest2 main function tests the PoissonRegression class.

The poissonRegressionTest2 main function tests the PoissonRegression class.

Attributes

See also

statmaster.sdu.dk/courses/st111/module03/index.html

www.stat.wisc.edu/~mchung/teaching/.../GLM.logistic.Rpackage.pdf

runMain scalation.modeling.poissonRegressionTest2

def polyORegressionTest(): Unit

The polyORegressionTest object tests PolyORegression class using the following regression equation. y = b dot x = b_0 + b_1t + b_2t^2 + ... b_k*t_k Note, the 'order' at which R-Squared drops is QR(7), Cholesky(14), SVD(6), Inverse(13).

The polyORegressionTest object tests PolyORegression class using the following regression equation. y = b dot x = b_0 + b_1t + b_2t^2 + ... b_k*t_k Note, the 'order' at which R-Squared drops is QR(7), Cholesky(14), SVD(6), Inverse(13).

runMain scalation.modeling.polyORegressionTest

Attributes

def polyORegressionTest2(): Unit

The polyORegressionTest2 object tests PolyORegression class using the following regression equation. y = b dot x = b_0 + b_1t + b_2t^2 + ... b_k*t_k

The polyORegressionTest2 object tests PolyORegression class using the following regression equation. y = b dot x = b_0 + b_1t + b_2t^2 + ... b_k*t_k

runMain scalation.modeling.polyORegressionTest2

Attributes

def polyRegressionTest(): Unit

The polyRegressionTest main function tests PolyRegression class using the following regression equation. y = b dot x = b_0 + b_1t + b_2t^2 + ... b_k*t_k Note, the order at which R-Squared drops is QR(7), Cholesky(14), SVD(6), Inverse(13).

The polyRegressionTest main function tests PolyRegression class using the following regression equation. y = b dot x = b_0 + b_1t + b_2t^2 + ... b_k*t_k Note, the order at which R-Squared drops is QR(7), Cholesky(14), SVD(6), Inverse(13).

runMain scalation.modeling.polyRegressionTest

Attributes

def polyRegressionTest2(): Unit

The polyRegressionTest2 main function tests PolyRegression class using the following regression equation. y = b dot x = b_0 + b_1t + b_2t^2 + ... b_k*t_k

The polyRegressionTest2 main function tests PolyRegression class using the following regression equation. y = b dot x = b_0 + b_1t + b_2t^2 + ... b_k*t_k

runMain scalation.modeling.polyRegressionTest2

Attributes

def predictorTest(): Unit

The predictorTest main function is used to test the Predictor trait and its derived classes using the Example_AutoMPG dataset containing data matrices x, ox and response vector y. Shift imports for the Example_BasketBall or Example_BPressure datasets.

The predictorTest main function is used to test the Predictor trait and its derived classes using the Example_AutoMPG dataset containing data matrices x, ox and response vector y. Shift imports for the Example_BasketBall or Example_BPressure datasets.

Attributes

See also

`Example_AutoMPG_Correlation

runMain scalation.modeling.predictorTest

def regressionCatTest(): Unit

The regressionCatTest main function tests the RegressionCat class using the following regression equation. y = b dot x = b_0 + b_1x_1 + b_2x_2 + b_3d_1 + b_4d_2

The regressionCatTest main function tests the RegressionCat class using the following regression equation. y = b dot x = b_0 + b_1x_1 + b_2x_2 + b_3d_1 + b_4d_2

runMain scalation.modeling.regressionCatTest

Attributes

def regressionCatTest2(): Unit

The regressionCatTest2 main function tests the RegressionCat class using the following regression equation.

The regressionCatTest2 main function tests the RegressionCat class using the following regression equation.

y  =  b dot x  =  b_0 + b_1*x_1 + b_2*x_2 + b_3*d_1 + b_4*d_2

This version needs the treatment levels to be shift down to zero.

runMain scalation.modeling.regressionCatTest2

Attributes

def regressionCatTest3(): Unit

The regressionCatTest3 main function tests the RegressionCat object related to related to encoding a column x1 of strings.

The regressionCatTest3 main function tests the RegressionCat object related to related to encoding a column x1 of strings.

runMain scalation.modeling.regressionCatTest3

Attributes

def regressionCatTest4(): Unit

The regressionCatTest4 main function tests the RegressionCat class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

The regressionCatTest4 main function tests the RegressionCat class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

runMain scalation.modeling.regressionCatTest4

Attributes

def regressionCatTest5(): Unit

The regressionCatTest5 main function tests the RegressionCat class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

The regressionCatTest5 main function tests the RegressionCat class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

runMain scalation.modeling.regressionCatTest5

Attributes

def regressionTest(): Unit

The regressionTest main function tests Regression class using the following regression equation. y = b dot x = b_0 + b_1x_1 + b_2x_2.

The regressionTest main function tests Regression class using the following regression equation. y = b dot x = b_0 + b_1x_1 + b_2x_2.

Attributes

See also

statmaster.sdu.dk/courses/st111/module03/index.html

runMain scalation.modeling.regressionTest

def regressionTest2(): Unit

The regressionTest2 main function is used to test the correctness of the factorization algorithms used to solve for the parameters b in Regression.

The regressionTest2 main function is used to test the correctness of the factorization algorithms used to solve for the parameters b in Regression.

Attributes

See also

scalation.mathstat.Fac_QRTest2

runMain scalation.modeling.regressionTest2

def regressionTest3(): Unit

The regressionTest3 main function tests the Regression class using the AutoMPG dataset. Assumes no missing values. It test cross validation.

The regressionTest3 main function tests the Regression class using the AutoMPG dataset. Assumes no missing values. It test cross validation.

runMain scalation.modeling.regressionTest3

Attributes

def regressionTest4(): Unit

The regressionTest4 main function tests the Regression class using the AutoMPG dataset. Assumes no missing values. It tests forward selection.

The regressionTest4 main function tests the Regression class using the AutoMPG dataset. Assumes no missing values. It tests forward selection.

runMain scalation.modeling.regressionTest4

Attributes

def regressionTest5(): Unit

The regressionTest5 main function tests the Regression class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

The regressionTest5 main function tests the Regression class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

runMain scalation.modeling.regressionTest5

Attributes

def regressionTest6(): Unit

The regressionTest6 main function tests the Regression class using the following regression equation. y = b dot x = b_0 + b_1x1 + b_2x_2. Show effects of increasing collinearity.

The regressionTest6 main function tests the Regression class using the following regression equation. y = b dot x = b_0 + b_1x1 + b_2x_2. Show effects of increasing collinearity.

runMain scalation.modeling.regressionTest6

Attributes

def regressionTest7(): Unit

The regressionTest7 main function trains a regression model on a small dataset of temperatures from counties in Texas where the variables/factors to consider are Latitude (x1), Elevation (x2) and Longitude (x3). The model equation is the following: y = b dot x = b0 + b1x1 + b2x2 + b3*x3

The regressionTest7 main function trains a regression model on a small dataset of temperatures from counties in Texas where the variables/factors to consider are Latitude (x1), Elevation (x2) and Longitude (x3). The model equation is the following: y = b dot x = b0 + b1x1 + b2x2 + b3*x3

runMain scalation.modeling.regressionTest7

Attributes

def regressionTreeGBTest(): Unit

The regressionTreeGBTest main function is used to test the RegressionTreeGB class.

The regressionTreeGBTest main function is used to test the RegressionTreeGB class.

Attributes

See also

translate.google.com/translate?hl=en&sl=zh-CN&u=https: //www.hrwhisper.me/machine-learning-decision-tree/&prev=search

runMain scalation.modeling.regressionTreeGBTest

def regressionTreeGBTest2(): Unit

The regressionTreeGBTest2 main function tests the RegressionTreeGB class using the AutoMPG dataset. Assumes no missing values. It tests multiple depths.

The regressionTreeGBTest2 main function tests the RegressionTreeGB class using the AutoMPG dataset. Assumes no missing values. It tests multiple depths.

runMain scalation.modeling.regressionTreeGBTest2

Attributes

def regressionTreeGBTest3(): Unit

The regressionTreeGBTest3 main function tests the RegressionTreeGB class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

The regressionTreeGBTest3 main function tests the RegressionTreeGB class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

runMain scalation.modeling.regressionTreeGBTest3

Attributes

def regressionTreeGBTest4(): Unit

The regressionTreeGBTest4 main function is used to test the RegressionTreeGB class. on the Boston House Prices dataset. Use in-sample training testing.

The regressionTreeGBTest4 main function is used to test the RegressionTreeGB class. on the Boston House Prices dataset. Use in-sample training testing.

runMain scalation.modeling.regressionTreeGBTest4

Attributes

def regressionTreeGBTest5(): Unit

The regressionTreeGBTest5 main function is used to test the RegressionTreeGB class. on the Boston House Prices dataset. Use train and test split.

The regressionTreeGBTest5 main function is used to test the RegressionTreeGB class. on the Boston House Prices dataset. Use train and test split.

runMain scalation.modeling.regressionTreeGBTest5

Attributes

def regressionTreeGBTest6(): Unit

The regressionTreeGBTest6 main function is used to test the RegressionTreeGB class.

The regressionTreeGBTest6 main function is used to test the RegressionTreeGB class.

runMain scalation.modeling.regressionTreeGBTest6

Attributes

def regressionTreeMTTest(): Unit

The regressionTreeMTTest main function is used to test the RegressionTreeMT class.

The regressionTreeMTTest main function is used to test the RegressionTreeMT class.

Attributes

See also

translate.google.com/translate?hl=en&sl=zh-CN&u=https: //www.hrwhisper.me/machine-learning-decision-tree/&prev=search

runMain scalation.modeling.regressionTreeMTTest

def regressionTreeMTTest2(): Unit

The regressionTreeMTTest2 main function tests the RegressionTreeMT class using the AutoMPG dataset. Assumes no missing values. It tests multiple depths.

The regressionTreeMTTest2 main function tests the RegressionTreeMT class using the AutoMPG dataset. Assumes no missing values. It tests multiple depths.

runMain scalation.modeling.regressionTreeMTTest2

Attributes

def regressionTreeMTTest3(): Unit

The regressionTreeMTTest3 main function tests the RegressionTreeMT class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

The regressionTreeMTTest3 main function tests the RegressionTreeMT class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

runMain scalation.modeling.regressionTreeMTTest3

Attributes

def regressionTreeRFTest(): Unit

The regressionTreeRFTest main function is used to test the RegressionTreeRF class.

The regressionTreeRFTest main function is used to test the RegressionTreeRF class.

Attributes

See also

translate.google.com/translate?hl=en&sl=zh-CN&u=https: //www.hrwhisper.me/machine-learning-decision-tree/&prev=search

runMain scalation.modeling.regressionTreeRFTest

def regressionTreeRFTest2(): Unit

The regressionTreeRFTest2 main function tests the RegressionTreeRF class using the AutoMPG dataset. Assumes no missing values. It tests multiple depths.

The regressionTreeRFTest2 main function tests the RegressionTreeRF class using the AutoMPG dataset. Assumes no missing values. It tests multiple depths.

runMain scalation.modeling.regressionTreeRFTest2

Attributes

def regressionTreeRFTest3(): Unit

The regressionTreeRFTest3 main function tests the RegressionTreeRF class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

The regressionTreeRFTest3 main function tests the RegressionTreeRF class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

runMain scalation.modeling.regressionTreeRFTest3

Attributes

def regressionTreeRFTest4(): Unit

The regressionTreeRFTest4 main function tests the RegressionTreeRF class using the Boston House Prices dataset.

The regressionTreeRFTest4 main function tests the RegressionTreeRF class using the Boston House Prices dataset.

runMain scalation.modeling.regressionTreeRFTest4

Attributes

def regressionTreeTest(): Unit

The regressionTreeTest main function is used to test the RegressionTree class. It tests a simple case that does not require a file to be read.

The regressionTreeTest main function is used to test the RegressionTree class. It tests a simple case that does not require a file to be read.

Attributes

See also

translate.google.com/translate?hl=en&sl=zh-CN&u=https: //www.hrwhisper.me/machine-learning-decision-tree/&prev=search

runMain scalation.modeling.regressionTreeTest

def regressionTreeTest2(): Unit

The regressionTreeTest2 main function tests the RegressionTree class using the AutoMPG dataset. Assumes no missing values. It tests multiple depths.

The regressionTreeTest2 main function tests the RegressionTree class using the AutoMPG dataset. Assumes no missing values. It tests multiple depths.

runMain scalation.modeling.regressionTreeTest2

Attributes

def regressionTreeTest3(): Unit

The regressionTreeTest3 main function tests the RegressionTree class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

The regressionTreeTest3 main function tests the RegressionTree class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection.

runMain scalation.modeling.regressionTreeTest3

Attributes

def regressionTreeTest4(): Unit

The regressionTreeTest4 main function tests the RegressionTree class using the Boston House Prices dataset.

The regressionTreeTest4 main function tests the RegressionTree class using the Boston House Prices dataset.

runMain scalation.modeling.regressionTreeTest4

Attributes

def regressionWLSTest(): Unit

The regressionWLSTest main function tests RegressionWLS class using the following regression equation. y = b dot x = b_0 + b_1x_1 + b_2x_2.

The regressionWLSTest main function tests RegressionWLS class using the following regression equation. y = b dot x = b_0 + b_1x_1 + b_2x_2.

Attributes

See also

statmaster.sdu.dk/courses/st111/module03/index.html

runMain scalation.modeling.regressionWLSTest

def regressionWLSTest2(): Unit

The regressionWLSTest2 main function tests the RegressionWLS class using the AutoMPG dataset. Assumes no missing values. It test cross validation.

The regressionWLSTest2 main function tests the RegressionWLS class using the AutoMPG dataset. Assumes no missing values. It test cross validation.

runMain scalation.modeling.regressionWLSTest2

Attributes

def ridgeRegressionTest(): Unit

The ridgeRegressionTest main function tests the RidgeRegression class using the following regression equation. y = b dot x = b_1x_1 + b_2x_2. It compares RidgeRegression with Regression

The ridgeRegressionTest main function tests the RidgeRegression class using the following regression equation. y = b dot x = b_1x_1 + b_2x_2. It compares RidgeRegression with Regression

Attributes

See also

statmaster.sdu.dk/courses/st111/module03/index.html

runMain scalation.modeling.ridgeRegressionTest

def ridgeRegressionTest2(): Unit

The ridgeRegressionTest2 main function tests the RidgeRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2. Try non-default value for the 'lambda' hyper-parameter.

The ridgeRegressionTest2 main function tests the RidgeRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2. Try non-default value for the 'lambda' hyper-parameter.

runMain scalation.modeling.ridgeRegressionTest2

Attributes

def ridgeRegressionTest3(): Unit

The ridgeRegressionTest3 main function tests the RidgeRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2 Test regression, forward selection and backward elimination.

The ridgeRegressionTest3 main function tests the RidgeRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2 Test regression, forward selection and backward elimination.

runMain scalation.modeling.ridgeRegressionTest3

Attributes

def ridgeRegressionTest4(): Unit

The ridgeRegressionTest4 main function tests the RidgeRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2

The ridgeRegressionTest4 main function tests the RidgeRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2

runMain scalation.modeling.ridgeRegressionTest4

Attributes

def ridgeRegressionTest5(): Unit

The ridgeRegressionTest5 main function tests the RidgeRegression class using the AutoMPG dataset. Assumes no missing values. It also combines feature selection with cross-validation and plots R^2, R^2 bar and R^2 cv vs. the instance index. Note, since x0 is automatically included in feature selection, make it an important variable.

The ridgeRegressionTest5 main function tests the RidgeRegression class using the AutoMPG dataset. Assumes no missing values. It also combines feature selection with cross-validation and plots R^2, R^2 bar and R^2 cv vs. the instance index. Note, since x0 is automatically included in feature selection, make it an important variable.

runMain scalation.modeling.ridgeRegressionTest5

Attributes

def ridgeRegressionTest6(): Unit

The ridgeRegressionTest6 main function tests the multi-collinearity method in the RidgeRegression class using the following regression equation. y = b dot x = b_1x_1 + b_2x_2 + b_3*x_3 + b_4 * x_4

The ridgeRegressionTest6 main function tests the multi-collinearity method in the RidgeRegression class using the following regression equation. y = b dot x = b_1x_1 + b_2x_2 + b_3*x_3 + b_4 * x_4

Attributes

See also

online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html

online.stat.psu.edu/online/development/stat501/data/bloodpress.txt

runMain scalation.modeling.ridgeRegressionTest6

def roundRegressionTest(): Unit

The roundRegressionTest main function tests RoundRegression class using the following regression equation. y = round (b dot x) = round (b_0 + b_1x_1 + b_2x_2).

The roundRegressionTest main function tests RoundRegression class using the following regression equation. y = round (b dot x) = round (b_0 + b_1x_1 + b_2x_2).

runMain scalation.modeling.roundRegressionTest

Attributes

def scale(extremes: (VectorD, VectorD), bounds: (Double, Double))(x: MatrixD): MatrixD

Scale matrix x to the range lb to ub, column-wise: x -> x_s.

Scale matrix x to the range lb to ub, column-wise: x -> x_s.

Value parameters

bounds

the desired (lower, upper) bounds

extremes

the (min_x, max_x) vectors of original matrix x where min_x the vector of column minima of matrix x max_x the vector of column maxima of matrix x

x

the matrix to scale

Attributes

def scaleV(extremes: (Double, Double), bounds: (Double, Double))(x: VectorD): VectorD

Scale vector x to the range lb to ub: x -> x_s.

Scale vector x to the range lb to ub: x -> x_s.

Value parameters

bounds

the desired (lower, upper) bounds

extremes

the (minimum value, maximum value) in vector x

x

the vector to scale

Attributes

def simpleExpRegressionTest(): Unit

The simpleExpRegressionTest main function tests SimpleExpRegression class using the following exponential regression problem.

The simpleExpRegressionTest main function tests SimpleExpRegression class using the following exponential regression problem.

runMain scalation.modeling.simpleExpRegressionTest

Attributes

def simpleExpRegressionTest2(): Unit

The SimpleExpRegressionTest2 main function tests the SimpleExpRegression class.

The SimpleExpRegressionTest2 main function tests the SimpleExpRegression class.

runMain scalation.modeling.simpleExpRegressionTest2

Attributes

def simpleExpRegressionTest3(): Unit

The simpleExpRegressionTest3 main function tests the SimpleExpRegression class.

The simpleExpRegressionTest3 main function tests the SimpleExpRegression class.

Attributes

See also

http://www.cnachtsheim-text.csom.umn.edu/kut86916_ch13.pdf y = 58.6065 exp (-.03959 x) + e

runMain scalation.modeling.simpleExpRegressionTest3

def simpleRegressionTest(): Unit

The simpleRegressionTest main function to test the SimpleRegression class. y = b0 + b1 * x

The simpleRegressionTest main function to test the SimpleRegression class. y = b0 + b1 * x

runMain scalation.modeling.simpleRegressionTest

Attributes

def simpleRegressionTest2(): Unit

The simpleRegressionTest2 main function to test the SimpleRegression class. y = b0 + b1 * x

The simpleRegressionTest2 main function to test the SimpleRegression class. y = b0 + b1 * x

runMain scalation.modeling.simpleRegressionTest2

Attributes

def simpleRegressionTest3(): Unit

The simpleRegressionTest3 main function is used to test the SimpleRegression class. y = b dot x = [b0, b1] dot [1, x1]

The simpleRegressionTest3 main function is used to test the SimpleRegression class. y = b dot x = [b0, b1] dot [1, x1]

Attributes

See also

www.analyzemath.com/statistics/linear_regression.html

runMain scalation.modeling.simpleRegressionTest3

def simpleRegressionTest4(): Unit

The simpleRegressionTest4 main function is used to test the SimpleRegression class. y = b dot x = b0 + b1 * x1

The simpleRegressionTest4 main function is used to test the SimpleRegression class. y = b dot x = b0 + b1 * x1

Attributes

See also

mathbits.com/mathbits/tisection/Statistics2/linear.htm

runMain scalation.modeling.simpleRegressionTest4

def simpleRegressionTest5(): Unit

The simpleRegressionTest5 main function is used to test the SimpleRegression class. y = b dot x = b0 + b1 * x1 This version uses gradient descent to search for the optimal solution for b.

The simpleRegressionTest5 main function is used to test the SimpleRegression class. y = b dot x = b0 + b1 * x1 This version uses gradient descent to search for the optimal solution for b.

runMain scalation.modeling.simpleRegressionTest5

Attributes

def simpleRegressionTest6(): Unit

The simpleRegressionTest6 main function is used to test the SimpleRegression class. y = b dot x = b0 + b1 * x1 This version does Exploratory Data Analysis (EDA) on the AutoMPG dataset.

The simpleRegressionTest6 main function is used to test the SimpleRegression class. y = b dot x = b0 + b1 * x1 This version does Exploratory Data Analysis (EDA) on the AutoMPG dataset.

runMain scalation.modeling.simpleRegressionTest6

Attributes

def simpleRegressionTest7(): Unit

The simpleRegressionTest7 main function is used to test the SimpleRegression class. y = b dot x = b0 + b1 * x1^2 This version does Exploratory Data Analysis (EDA) on the AutoMPG dataset looking for quadratic patterns.

The simpleRegressionTest7 main function is used to test the SimpleRegression class. y = b dot x = b0 + b1 * x1^2 This version does Exploratory Data Analysis (EDA) on the AutoMPG dataset looking for quadratic patterns.

runMain scalation.modeling.simpleRegressionTest7

Attributes

def simpleRegressionTest8(): Unit

The simpleRegressionTest8 main function tests the SimpleRegression class using a simple dataset and compares it with the NullModel.

The simpleRegressionTest8 main function tests the SimpleRegression class using a simple dataset and compares it with the NullModel.

runMain scalation.modeling.simpleRegressionTest8

Attributes

def simplerRegressionTest(): Unit

The simplerRegressionTest main function is used to test the SimplerRegression class. y = b0 * x + e

The simplerRegressionTest main function is used to test the SimplerRegression class. y = b0 * x + e

runMain scalation.modeling.simplerRegressionTest

Attributes

def simplerRegressionTest2(): Unit

The simplerRegressionTest2 main function is used to test the SimplerRegression class. y = b dot x + e = [b0] dot [x0] + e

The simplerRegressionTest2 main function is used to test the SimplerRegression class. y = b dot x + e = [b0] dot [x0] + e

runMain scalation.modeling.simplerRegressionTest2

Attributes

def simplerRegressionTest3(): Unit

The simplerRegressionTest3 main function is used to test the SimplerRegression class. y = b dot x + e = [b0] dot [x0] + e

The simplerRegressionTest3 main function is used to test the SimplerRegression class. y = b dot x + e = [b0] dot [x0] + e

runMain scalation.modeling.simplerRegressionTest3

Attributes

def simplerRegressionTest4(): Unit

The simplerRegressionTest4 main function is used to test the SimplerRegression class. y = b dot x = b0 * x0

The simplerRegressionTest4 main function is used to test the SimplerRegression class. y = b dot x = b0 * x0

Attributes

See also

mathbits.com/mathbits/tisection/Statistics2/linear.htm

runMain scalation.modeling.simplerRegressionTest4

def subSample(x: MatrixD, nSamp: Int, stream: Int): (MatrixD, VectorI)

Create a random sub-sample of rows from matrix x, returning the sub-sample matrix and the indices selected. Must change the stream parameter to get a different subsample.

Create a random sub-sample of rows from matrix x, returning the sub-sample matrix and the indices selected. Must change the stream parameter to get a different subsample.

Value parameters

nSamp

the desired sample size (number of rows in matrix)

stream

the random number stream to use

x

the data original matrix

Attributes

def subSample(x: MatrixD, y: VectorD, nSamp: Int, stream: Int): (MatrixD, VectorD, VectorI)

Create a random sub-sample of rows from matrix x and vector y, returning the sub-sample matrix and vector and the indices selected.

Create a random sub-sample of rows from matrix x and vector y, returning the sub-sample matrix and vector and the indices selected.

Value parameters

nSamp

the desired sample size (number of rows in matrix)

stream

the random number stream to use

x

the original input/data matrix

y

the original output/response vector

Attributes

def subSample(x: MatrixD, y: VectorI, nSamp: Int, stream: Int): (MatrixD, VectorI, VectorI)

Create a random sub-sample of rows from matrix x and integer-valued vector y, returning the sub-sample matrix and vector and the indices selected.

Create a random sub-sample of rows from matrix x and integer-valued vector y, returning the sub-sample matrix and vector and the indices selected.

Value parameters

nSamp

the desired sample size (number of rows in matrix)

stream

the random number stream to use

x

the original input/data matrix

y

the original integer-valued output/response vector

Attributes

def sumQueueTest(): Unit

The sumQueueTest main function is used to test the SumQueue class.

The sumQueueTest main function is used to test the SumQueue class.

runMain scalation.modeling.sumQueueTest

Attributes

def sumQueueTest2(): Unit

The sumQueueTest2 main function is used to test the SumSqQueue class.

The sumQueueTest2 main function is used to test the SumSqQueue class.

runMain scalation.modeling.sumQueueTest2

Attributes

def symLassoRegressionTest(): Unit

The symLassoRegressionTest main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Lasso Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression.

The symLassoRegressionTest main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Lasso Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symLassoRegressionTest

Attributes

def symLassoRegressionTest2(): Unit

The symLassoRegressionTest2 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic Lasso Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

The symLassoRegressionTest2 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic Lasso Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symLassoRegressionTest2

Attributes

def symLassoRegressionTest3(): Unit

The symLassoRegressionTest3 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic X Lasso Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

The symLassoRegressionTest3 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic X Lasso Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symLassoRegressionTest3

Attributes

def symLassoRegressionTest4(): Unit

The symLassoRegressionTest4 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic Lasso Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

The symLassoRegressionTest4 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic Lasso Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symLassoRegressionTest4

Attributes

def symLassoRegressionTest5(): Unit

The symLassoRegressionTest5 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic X Lasso Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

The symLassoRegressionTest5 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic X Lasso Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symLassoRegressionTest5

Attributes

def symLassoRegressionTest6(): Unit

The symLassoRegressionTest6 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic XX Lasso Regression" (with cross, cross3 = true) and applies forward selection, backward elimination, or stepwise regression. WARNING: setting cross3 = true can lead to an explotion of terms.

The symLassoRegressionTest6 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic XX Lasso Regression" (with cross, cross3 = true) and applies forward selection, backward elimination, or stepwise regression. WARNING: setting cross3 = true can lead to an explotion of terms.

runMain scalation.modeling.symLassoRegressionTest6

Attributes

def symLassoRegressionTest7(): Unit

The symLassoRegressionTest7 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Lasso Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

The symLassoRegressionTest7 main function tests the SymLassoRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Lasso Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

runMain scalation.modeling.symLassoRegressionTest7

Attributes

def symLassoRegressionTest8(): Unit

The symLassoRegressionTest8 main function tests the SymLassoRegression object using a simulated gravity dataset. It tests custom "Symbolic Regression", with a custom term: x0 x1^(-2) FIX - acquire a real gravity dataset

The symLassoRegressionTest8 main function tests the SymLassoRegression object using a simulated gravity dataset. It tests custom "Symbolic Regression", with a custom term: x0 x1^(-2) FIX - acquire a real gravity dataset

runMain scalation.modeling.symLassoRegressionTest8

Attributes

def symLassoRegressionTest9(): Unit

The symLassoRegressionTest9 main function tests the SymLassoRegression object using a simple dataset to compare Lasso Regression, Quadratic Lasso Regression and Cubic Lasso Regression.

The symLassoRegressionTest9 main function tests the SymLassoRegression object using a simple dataset to compare Lasso Regression, Quadratic Lasso Regression and Cubic Lasso Regression.

runMain scalation.modeling.symLassoRegressionTest9

Attributes

def symRidgeRegressionTest(): Unit

The symRidgeRegressionTest main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Ridge Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression.

The symRidgeRegressionTest main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Ridge Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symRidgeRegressionTest

Attributes

def symRidgeRegressionTest2(): Unit

The symRidgeRegressionTest2 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic Ridge Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

The symRidgeRegressionTest2 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic Ridge Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symRidgeRegressionTest2

Attributes

def symRidgeRegressionTest3(): Unit

The symRidgeRegressionTest3 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic X Ridge Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

The symRidgeRegressionTest3 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic X Ridge Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symRidgeRegressionTest3

Attributes

def symRidgeRegressionTest4(): Unit

The symRidgeRegressionTest4 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic Ridge Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

The symRidgeRegressionTest4 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic Ridge Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symRidgeRegressionTest4

Attributes

def symRidgeRegressionTest5(): Unit

The symRidgeRegressionTest5 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic X Ridge Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

The symRidgeRegressionTest5 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic X Ridge Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symRidgeRegressionTest5

Attributes

def symRidgeRegressionTest6(): Unit

The symRidgeRegressionTest6 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic XX Ridge Regression" (with cross, cross3 = true) and applies forward selection, backward elimination, or stepwise regression. WARNING: setting cross3 = true can lead to an explotion of terms.

The symRidgeRegressionTest6 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic XX Ridge Regression" (with cross, cross3 = true) and applies forward selection, backward elimination, or stepwise regression. WARNING: setting cross3 = true can lead to an explotion of terms.

runMain scalation.modeling.symRidgeRegressionTest6

Attributes

def symRidgeRegressionTest7(): Unit

The symRidgeRegressionTest7 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Ridge Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

The symRidgeRegressionTest7 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Ridge Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

runMain scalation.modeling.symRidgeRegressionTest7

Attributes

def symRidgeRegressionTest8(): Unit

The symRidgeRegressionTest8 main function tests the SymRidgeRegression object using a simulated gravity dataset. It tests custom "Symbolic Regression", with a custom term: x0 x1^(-2) FIX - acquire a real gravity dataset

The symRidgeRegressionTest8 main function tests the SymRidgeRegression object using a simulated gravity dataset. It tests custom "Symbolic Regression", with a custom term: x0 x1^(-2) FIX - acquire a real gravity dataset

runMain scalation.modeling.symRidgeRegressionTest8

Attributes

def symRidgeRegressionTest9(): Unit

The symRidgeRegressionTest9 main function tests the SymRidgeRegression object using a simple dataset to compare Ridge Regression, Quadratic Ridge Regression and Cubic Ridge Regression.

The symRidgeRegressionTest9 main function tests the SymRidgeRegression object using a simple dataset to compare Ridge Regression, Quadratic Ridge Regression and Cubic Ridge Regression.

runMain scalation.modeling.symRidgeRegressionTest9

Attributes

def symbolicRegressionTest(): Unit

The symbolicRegressionTest main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression.

The symbolicRegressionTest main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symbolicRegressionTest

Attributes

def symbolicRegressionTest2(): Unit

The symbolicRegressionTest2 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

The symbolicRegressionTest2 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symbolicRegressionTest2

Attributes

def symbolicRegressionTest3(): Unit

The symbolicRegressionTest3 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic X Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

The symbolicRegressionTest3 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Quadratic X Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symbolicRegressionTest3

Attributes

def symbolicRegressionTest4(): Unit

The symbolicRegressionTest4 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

The symbolicRegressionTest4 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic Regression" (with cross = false) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symbolicRegressionTest4

Attributes

def symbolicRegressionTest5(): Unit

The symbolicRegressionTest5 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic X Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

The symbolicRegressionTest5 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic X Regression" (with cross = true) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symbolicRegressionTest5

Attributes

def symbolicRegressionTest6(): Unit

The symbolicRegressionTest6 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic XX Regression" (with cross, cross3 = true) and applies forward selection, backward elimination, or stepwise regression. WARNING: setting cross3 = true can lead to an explotion of terms.

The symbolicRegressionTest6 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests "Cubic XX Regression" (with cross, cross3 = true) and applies forward selection, backward elimination, or stepwise regression. WARNING: setting cross3 = true can lead to an explotion of terms.

runMain scalation.modeling.symbolicRegressionTest6

Attributes

def symbolicRegressionTest7(): Unit

The symbolicRegressionTest7 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

The symbolicRegressionTest7 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Regression", with powers specified in "Set (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

runMain scalation.modeling.symbolicRegressionTest7

Attributes

def symbolicRegressionTest8(): Unit

The symbolicRegressionTest8 main function tests the SymbolicRegression object using a simulated gravity dataset. It tests custom "Symbolic Regression", with a custom term: x0 x1^(-2) FIX - acquire a real gravity dataset

The symbolicRegressionTest8 main function tests the SymbolicRegression object using a simulated gravity dataset. It tests custom "Symbolic Regression", with a custom term: x0 x1^(-2) FIX - acquire a real gravity dataset

runMain scalation.modeling.symbolicRegressionTest8

Attributes

def symbolicRegressionTest9(): Unit

The symbolicRegressionTest9 main function tests the SymbolicRegression object using a simple dataset to compare Regression, Quadratic Regression and Cubic Regression.

The symbolicRegressionTest9 main function tests the SymbolicRegression object using a simple dataset to compare Regression, Quadratic Regression and Cubic Regression.

runMain scalation.modeling.symbolicRegressionTest9

Attributes

def tranRegressionTest(): Unit

The tranRegressionTest main function tests TranRegression class using the following regression equation. log (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

The tranRegressionTest main function tests TranRegression class using the following regression equation. log (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

runMain scalation.modeling.tranRegressionTest

Attributes

def tranRegressionTest2(): Unit

The tranRegressionTest2 main function tests TranRegression class using the following regression equation. sqrt (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

The tranRegressionTest2 main function tests TranRegression class using the following regression equation. sqrt (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

runMain scalation.modeling.tranRegressionTest2

Attributes

def tranRegressionTest3(): Unit

The tranRegressionTest3 main function tests TranRegression class using the following regression equation and uses the simulated data in TranRegressionEx.. sqrt (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

The tranRegressionTest3 main function tests TranRegression class using the following regression equation and uses the simulated data in TranRegressionEx.. sqrt (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

Attributes

See also

6.12.9 exercises 1, 2, and 3.

runMain scalation.modeling.tranRegressionTest3

def tranRegressionTest4(): Unit

The tranRegressionTest4 main function tests TranRegression class using the following regression equation. sqrt (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

The tranRegressionTest4 main function tests TranRegression class using the following regression equation. sqrt (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

runMain scalation.modeling.tranRegressionTest4

Attributes

def tranRegressionTest5(): Unit

The tranRegressionTest5 main function tests TranRegression class using the following regression equation. sigmoid^{-1} (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

The tranRegressionTest5 main function tests TranRegression class using the following regression equation. sigmoid^{-1} (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

runMain scalation.modeling.tranRegressionTest5

Attributes

def tranRegressionTest6(): Unit

The tranRegressionTest6 main function tests TranRegression class using the following regression equation on the beer foam dataset.

The tranRegressionTest6 main function tests TranRegression class using the following regression equation on the beer foam dataset.

Attributes

See also

https://www.tf.uni-kiel.de/matwis/amat/iss/kap_2/articles/beer_article.pdf exp (y) = b dot x = b_0 + b_1*x_1.

runMain scalation.modeling.tranRegressionTest6

def tranRegressionTest7(): Unit

The tranRegressionTest7 main function tests the TranRegression class using the AutoMPG dataset. It also combines feature selection with cross-validation and plots R^2, R^2 bar and R^2 cv vs. the instance index.

The tranRegressionTest7 main function tests the TranRegression class using the AutoMPG dataset. It also combines feature selection with cross-validation and plots R^2, R^2 bar and R^2 cv vs. the instance index.

runMain scalation.modeling.tranRegressionTest7

Attributes

def tranRegressionTest8(): Unit

The tranRegressionTest8 main function tests and compares Regression vs. SymbolicRegression.quadratic vs. TranRegression. using the following regression equations. y = b dot x = b_0 + b_1x y = b dot x' = b_0 + b_1x + b_2x^2 y = b dot x' = b_0 + b_1x + b_2x^2 + b_3x^3

The tranRegressionTest8 main function tests and compares Regression vs. SymbolicRegression.quadratic vs. TranRegression. using the following regression equations. y = b dot x = b_0 + b_1x y = b dot x' = b_0 + b_1x + b_2x^2 y = b dot x' = b_0 + b_1x + b_2x^2 + b_3x^3

runMain scalation.modeling.tranRegressionTest8

Attributes

def trigRegressionTest(): Unit

The trigRegressionTest main function tests TrigRegression class using the following regression equation.

The trigRegressionTest main function tests TrigRegression class using the following regression equation.

y  =  b dot x  =  b_0 + b_1 sin wt + b_2 cos wt + ... b_2k-1 sin kwt + b_2k cos kwt + e

The data is generated from a noisy cubic function.

runMain scalation.modeling.trigRegressionTest

Attributes

def trigRegressionTest2(): Unit

The trigRegressionTest2 main function tests TrigRegression class using the following regression equation. y = b dot x = b_0 + b_1 sin wt + b_2 cos wt + ... b_2k-1 sin kwt + b_2k cos kwt + e The data is generated from periodic noisy cubic functions.

The trigRegressionTest2 main function tests TrigRegression class using the following regression equation. y = b dot x = b_0 + b_1 sin wt + b_2 cos wt + ... b_2k-1 sin kwt + b_2k cos kwt + e The data is generated from periodic noisy cubic functions.

runMain scalation.modeling.trigRegressionTest2

Attributes

def uncenter(x_c: MatrixD, mu_x: VectorD): MatrixD

Uncenter matrix x_c from zero mean, column-wise, by adding the mean.

Uncenter matrix x_c from zero mean, column-wise, by adding the mean.

Value parameters

mu_x

the vector of column means of matrix x_c

x_c

the matrix to uncenter

Attributes

def unscale(extremes: (VectorD, VectorD), bounds: (Double, Double))(x_s: MatrixD): MatrixD

Unscale matrix x_s from the range lb to ub, column-wise: x_s -> x.

Unscale matrix x_s from the range lb to ub, column-wise: x_s -> x.

Value parameters

bounds

the scaled (lower, upper) bounds

extremes

the (min_x, max_x) vectors of original matrix x where min_x the vector of column minima of matrix x max_x the vector of column maxima of matrix x

x_s

the matrix to unscale

Attributes

def unscaleV(extremes: (Double, Double), bounds: (Double, Double))(x_s: VectorD): VectorD

Unscale vector x_s from the range lb to ub to original range: x_s -> x.

Unscale vector x_s from the range lb to ub to original range: x_s -> x.

Value parameters

bounds

the scaled (lower, upper) bounds

extremes

the (minimum value, maximum value) in original vector x

x_s

the vector to unscale

Attributes

def variableTest(): Unit

The variableTest the conversion of a categorical variable into multiple dummy variables.

The variableTest the conversion of a categorical variable into multiple dummy variables.

runMain scalation.modeling.variableTest

Attributes

Concrete fields

val qoFI_all_names: Array[String]
val qoFI_names: Array[String]
val qoF_names: Array[String]
Generated with