analytics

package analytics

The analytics package contains classes, traits and objects for analytics including clustering and prediction.

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class ANCOVA extends Predictor with Error
The ANCOVA class supports ANalysis of COVAriance 'ANCOVA'.
The ANCOVA class supports ANalysis of COVAriance 'ANCOVA'. It allows the addition of a categorical treatment variable '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 (.)

See also
see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
class ANOVA1 extends PredictorVec
The ANOVA1 class supports one-way ANalysis Of VAriance (ANOVA), i.e, it allows only one binary/categorial treatment variable.
The ANOVA1 class supports one-way ANalysis Of VAriance (ANOVA), i.e, it allows only one binary/categorial treatment variable. It is framed using General Linear Model 'GLM' notation and supports the use of one binary/categorical treatment variable 't'. This is done by introducing dummy variables 'd_j' to distinguish the treatment level. The problem is again to fit the parameter vector 'b' in the following equation
y = b dot x + e = b_0 + b_1 * d_1 + b_1 * d_2 ... b_k * d_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 (.)

See also
psych.colorado.edu/~carey/Courses/PSYC5741/handouts/GLM%20Theory.pdf
ANCOVA for models with multiple variables
class CanCorrelation extends Reducer with Error
The CanCorrelation class performs Canonical Correlation Analysis 'CCA' on two random vectors.
The CanCorrelation class performs Canonical Correlation Analysis 'CCA' on two random vectors. Samples for the first one are stored in the 'x' data matrix and samples for the second are stored in the 'y' data matrix. Find vectors a and b that maximize the correlation between x * a and y * b.
max {rho (x * a, y * b)}
Additional vectors orthogonal to a and b can also be found.
class ExpRegression extends PredictorMat
The ExpRegression class supports exponential regression.
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

See also
www.stat.uni-muenchen.de/~leiten/Lehre/Material/GLM_0708/chapterGLM.pdf
class Fit extends AnyRef
The Fit class provides methods to determine basic quality of fit measures.
trait GLM extends AnyRef
A General Linear Model 'GLM' can be developed using the GLM trait and object (see below).
A General Linear Model 'GLM' can be developed using the GLM trait and object (see below). The implementation currently supports univariate models with multivariate models (where each response is a vector) planned for the future. It provides factory methods for the following special types of GLMs: SimpleRegression - simple linear regression, Regression - multiple linear regression using Ordinary Least Squares 'OLS' Regression_WLS - multiple linear regression using Weighted Least Squares 'WLS' RidgeRegression - robust multiple linear regression, TranRegression - transformed (e.g., log) multiple linear regression, PolyRegression - polynomial regression, TrigRegression - trigonometric regression ResponseSurface - response surface regression, ANOVA1 - GLM form of ANalysis Of VAriance, ANCOVA - GLM form of ANalysis of COVAriance.
class LassoRegression extends PredictorMat
The LassoRegression class supports multiple linear regression.
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).

See also
see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
class NMFactorization extends AnyRef
The NMFactorization class factors a matrix 'v' into two non negative matrices 'w' and 'h' such that 'v = wh' approximately.
The NMFactorization class factors a matrix 'v' into two non negative matrices 'w' and 'h' such that 'v = wh' approximately.

See also
en.wikipedia.org/wiki/Non-negative_matrix_factorization
abstract class NeuralNet extends Predictor with Error
The NeuralNet abstract class provides the basic structure and API for a variety of Neural Networks.
class NeuralNet_2L extends NeuralNet
The NeuralNet_2L class supports multi-output, 2-layer (input and output) Neural-Networks.
The NeuralNet_2L class supports multi-output, 2-layer (input and output) Neural-Networks. It can be used for both classification and prediction, depending on the activation functions used. Given several input vectors and output vectors (training data), fit the weights/parameters 'bb' connecting the layers, so that for a new input vector 'z', the net can predict the output value, i.e.,
yp_j = f (bb dot z)
where 'f' is the activation function and the parameter matrix 'bb' gives the weights between input and output layers. Note, 'b0' is treated as the bias, so 'x0' must be 1.0.
class NeuralNet_3L extends NeuralNet
The NeuralNet_3L class supports multi-output, 3-layer (input, hidden and output) Neural-Networks.
The NeuralNet_3L class supports multi-output, 3-layer (input, hidden and output) Neural-Networks. It can be used for both classification and prediction, depending on the activation functions used. Given several input vectors and output vectors (training data), fit the weights/parameters 'aa' and 'bb' connecting the layers, so that for a new input vector 'v', the net can predict the output value, i.e.,
yp = f2 (bb * f1V (aa * v))
where 'f1' and 'f2' are the activation functions and the parameter matrices 'aa' and 'bb' gives the weights between input-hidden and hidden-output layers. Note, if 'a0' is to be treated as bias/intercept, 'x0' must be 1.0.
class NeuralNet_XL extends Predictor with Error
The NeuralNet_XL class supports basic 3-layer (input, hidden and output) Neural Networks.
The NeuralNet_XL class supports basic 3-layer (input, hidden and output) Neural Networks. Given several input and output vectors (training data), fit the weights connecting the layers, so that for a new input vector 'zi', the net can predict the output vector 'zo' ('zh' is the intermediate value at the hidden layer), i.e.,
zi --> zh = f (w * zi) --> zo = g (v * zh)
Note, w_0 and v_0 are treated as biases, so zi_0 and zh_0 must be 1.0.
class NonLinRegression extends PredictorMat
The NonLinRegression class supports non-linear regression.
The NonLinRegression class supports non-linear regression. In this case, 'x' can be multi-dimensional '[1, x1, ... xk]' and the function 'f' is non-linear 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 Non-linear Programming to minimize Sum of Squares Error 'SSE'.

See also
www.bsos.umd.edu/socy/alan/stats/socy602_handouts/kut86916_ch13.pdf
class NullModel extends Fit with Predictor with Error
The NullModel class implements the simplest type of predictive modeling technique that just predicts the response 'y' to be the mean.
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 regression equation
y = b dot x + e = b0 + e
where 'e' represents the residuals (the part not explained by the model).
class Perceptron extends PredictorMat
The Perceptron class supports single-output, 2-layer (input and output) Neural-Networks.
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.
class PoissonRegression extends PredictorMat
The PoissonRegression class supports Poisson regression.
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.

See also
see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
class PolyRegression extends PredictorVec
The PolyRegression class supports polynomial 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 (.)

See also
www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx
trait Predictor extends AnyRef
The Predictor trait provides a common framework for several predictors.
The Predictor trait provides a common framework for several predictors. A predictor is for potentially unbounded responses (real or integer). When the number of distinct responses is bounded by some relatively small integer 'k', a classifier is likdely more appropriate. Note, the 'train' method must be called first followed by 'eval'.
abstract class PredictorMat extends Fit with Predictor with Error
The PredictorMat abstract class supports multiple predictor analytics.
The PredictorMat abstract class supports multiple predictor analytics. In this case, '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
Note, "protected val" arguments requires by ResponseSurface.
abstract class PredictorVec extends Predictor with Error
The PredictorVec class supports term expanded regression.
The PredictorVec class supports term expanded regression. Fit the parameter vector 'b' in the regression equation. 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 (.)
class PrincipalComponents extends Reducer with Error
The PrincipalComponents class performs the Principal Component Analysis 'PCA' on data matrix 'x'.
The PrincipalComponents class performs the Principal Component Analysis 'PCA' on data matrix 'x'. It can be used to reduce the dimensionality of the data. First find the Principal Components 'PC's by calling 'findPCs' and then call 'reduce' to reduce the data (i.e., reduce matrix 'x' to a lower dimensionality matrix).
class QuadraticFit extends AnyRef
The QuadraticFit class uses multiple regression to fit a quadratic surface to the function 'f'.
The QuadraticFit class uses multiple regression to fit a quadratic surface to the function 'f'. This is useful when computing 'f' is costly, for example in simulation optimization. The fit is over a multi-dimensional grid and can be used for interpolation and limited extrapolation.
trait Reducer extends AnyRef
The Reducer trait provides a common framework for several data reduction algorithms.
class Regression extends PredictorMat
The Regression class supports multiple linear regression.
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 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

See also
en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)
see.stanford.edu/materials/lsoeldsee263/05-ls.pdf Note, not intended for use when the number of degrees of freedom 'df' is negative.
class Regression_WLS extends Regression
The Regression_WLS class supports weighted multiple linear regression.
The Regression_WLS class supports weighted multiple linear regression. In this case, 'xx' is multi-dimensional [1, xx_1, ... xx_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 xx + e = b_0 + b_1 * xx_1 + ... b_k * xx_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 'xx' is reweighted 'x = rootW * xx' and the response vector 'yy' is reweighted 'y = rootW * yy' where 'rootW' is the square root of the weights.

See also
www.markirwin.net/stat149/Lecture/Lecture3.pdf
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
class ResponseSurface extends Regression
The ResponseSurface class uses multiple regression to fit a quadratic/cubic surface to the data.
The ResponseSurface class uses multiple regression to fit a quadratic/cubic surface to the data. For example in 2D, the quadratic regression equation is
y = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_0^{2, x_1, x_0*x_1, x_1}2] + e

See also
scalation.metamodel.QuadraticFit
class RidgeRegression extends PredictorMat
The RidgeRegression class supports multiple linear ridge regression.
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

See also
statweb.stanford.edu/~tibs/ElemStatLearn/
class SimpleRegression extends PredictorMat
The SimpleRegression class supports simple linear regression.
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).
class SimpleTest[VecT <: VectoD] extends AnyRef
class SimplerRegression extends PredictorMat
The SimplerRegression class supports simpler linear regression.
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.

See also
SimpleRegression for both intercept and slope parameters
class TranRegression extends Regression
The TranRegression class supports transformed multiple linear 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.

See also
www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx
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'.
class TrigRegression extends PredictorVec
The TrigRegression class supports trigonometric 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 (.)

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

Value Members

val BASE_DIR: String
The relative path for base directory
object ANCOVATest extends App
The ANCOVATest object tests the ANCOVA class using the following regression equation.
The ANCOVATest object tests the ANCOVA 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
> runMain scalation.analytics.ANCOVATest
object ANOVA1Test extends App
The ANOVA1Test object tests the ANOVA1 class using the following regression equation.
The ANOVA1Test object tests the ANOVA1 class using the following regression equation.
y = b dot x = b_0 + b_1*d_1 + b_2*d_2
> runMain scalation.analytics.ANOVA1Test
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.

See also
en.wikipedia.org/wiki/Activation_function Convention: fun activation function (e.g., sigmoid) funV vector version of activation function (e.g., sigmoidV) funM matrix version of activation function (e.g., sigmoidM) funDV vector version of dervivative (e.g., sigmoidDV) funDM matrix version of dervivative (e.g., sigmoidDM) ------------------------------------------------------------------------------ Supports: id, reLU, tanh, sigmoid, gaussain, softmax Related functions: logistic, logit
object ActivationFunTest extends App
The ActivationFunTest is used to test the ActivationFun object.
The ActivationFunTest is used to test the ActivationFun object. > runMain scalation.analytics.ActivationFunTest
object ActivationFunTest2 extends App
The ActivationFunTest2 is used to test the ActivationFun object.
The ActivationFunTest2 is used to test the ActivationFun object.

See also
en.wikipedia.org/wiki/Softmax_function > runMain scalation.analytics.ActivationFunTest2
object ExampleConcrete
The ExampleConcrete class stores a medium-sized example dataset from the UCI Machine Learning Repository, "Abstract: Concrete is a highly complex material.
The ExampleConcrete class stores a medium-sized example dataset from the UCI Machine Learning Repository, "Abstract: Concrete is a highly complex material. The slump flow of concrete is not only determined by the water content, but that is also influenced by other concrete ingredients."
object ExampleConcreteTest extends App
The ExampleConcreteTest object is used to test the ExampleConcrete object.
The ExampleConcreteTest object is used to test the ExampleConcrete object. It compares Regression, Perceptron, and NeuralNet_2L. This one runs Regression > runMain scalation.analytics.ExampleConcreteTest
object ExampleConcreteTest2 extends App
The ExampleConcreteTest2 object is used to test the ExampleConcrete object.
The ExampleConcreteTest2 object is used to test the ExampleConcrete object. It compares Regression, Perceptron, and NeuralNet_2L. This one runs Perceptron > runMain scalation.analytics.ExampleConcreteTest2
object ExampleConcreteTest3 extends App
The ExampleConcreteTest3 object is used to test the ExampleConcrete object.
The ExampleConcreteTest3 object is used to test the ExampleConcrete object. It compares Regression, Perceptron, and NeuralNet_2L. This one runs NeuralNet_2L with 'sigmoid' > runMain scalation.analytics.ExampleConcreteTest3
object ExampleConcreteTest4 extends App
The ExampleConcreteTest4 object is used to test the ExampleConcrete object.
The ExampleConcreteTest4 object is used to test the ExampleConcrete object. It compares Regression, Perceptron, and NeuralNet_2L. This one runs NeuralNet_2L with 'tanh' > runMain scalation.analytics.ExampleConcreteTest4
object ExampleConcreteTest5 extends App
The ExampleConcreteTest5 object is used to test the ExampleConcrete object.
The ExampleConcreteTest5 object is used to test the ExampleConcrete object. It compares Regression, Perceptron, and NeuralNet_2L. This one runs NeuralNet_2L with 'id' > runMain scalation.analytics.ExampleConcreteTest5
object ExampleConcreteTest6 extends App
The ExampleConcreteTest6 object is used to test the ExampleConcrete object.
The ExampleConcreteTest6 object is used to test the ExampleConcrete object. It compares Regression, Perceptron, NeuralNet_2L, and NeuralNet_3L. This one runs NeuralNet_3L with 'sigmoid' > runMain scalation.analytics.ExampleConcreteTest6
object ExpRegressionTest extends App
The ExpRegressionTest object tests ExpRegression class using the following exponential regression problem.
The ExpRegressionTest object tests ExpRegression class using the following exponential regression problem. > runMain scalation.analytics.ExpRegressionTest
object ExpRegressionTest2 extends App
The ExpRegressionTest2 object has a basic test for the ExpRegression class.
The ExpRegressionTest2 object has a basic test for the ExpRegression class. > runMain scalation.analytics.ExpRegressionTest
object Fit
The Fit companion object provides factory methods for assessing quality of fit for standard types of modeling techniques.
object GLM extends GLM
The GLM object makes the GLM trait's methods directly available.
The GLM object makes the GLM trait's methods directly available. This approach (using traits and objects) allows the methods to also be inherited.
object GLMTest extends App
The GLMTest object tests the GLM object using the following regression equation.
The GLMTest object tests the GLM object 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
object GZLM extends GLM
A Generalized Linear Model 'GZLM' can be developed using the GZLM object.
A Generalized Linear Model 'GZLM' can be developed using the GZLM object. It provides factory methods for General Linear Models 'GLM' via inheritance and for proper Generalized Linear Models: LogisticRegression - logistic regression, (@see classifier package) PoissonRegression - Poisson regression, ExpRegression - Exponential regression,
object GZLMTest extends App
The GZLMTest object tests the GZLM object using the following regression equation.
The GZLMTest object tests the GZLM object 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
object LassoRegressionTest extends App
The LassoRegressionTest object tests LassoRegression class using the following regression equation.
The LassoRegressionTest object tests LassoRegression class using the following regression equation.
y = b dot x = b_0 + b_1*x_1 + b_2*x_2.

See also
http://statmaster.sdu.dk/courses/st111/module03/index.html > runMain scalation.analytics.LassoRegressionTest
object MatrixTransform
The MatrixTransform object is used to transform the columns of a data matrix 'x'.
The MatrixTransform object is used to transform the columns of a data matrix 'x'. Such pre-processing of the data is required by some modeling techniques.
object MatrixTransformTest extends App
The MatrixTransformTest is used to test the MatrixTransform object.
The MatrixTransformTest is used to test the MatrixTransform object. > runMain scalation.analytics.MatrixTransformTest
object NMFactorizationTest extends App
The NMFactorizationTest object to test NMFactorizationTest class.
object NeuralNet_2LTest extends App
The NeuralNet_2LTest object is used to test the NeuralNet_2L class.
The NeuralNet_2LTest object is used to test the NeuralNet_2L class. For this test, training data is used to fit the weights before using them for prediction.

See also
www4.rgu.ac.uk/files/chapter3%20-%20bp.pdf > runMain scalation.analytics.NeuralNet_2LTest
object NeuralNet_3LTest extends App
The NeuralNet_3LTest object is used to test the NeuralNet_3L class.
The NeuralNet_3LTest object is used to test the NeuralNet_3L class. For this test, training data is used to fit the weights before using them for prediction.

See also
www4.rgu.ac.uk/files/chapter3%20-%20bp.pdf > runMain scalation.analytics.NeuralNet_3LTest
object NeuralNet_XLTest extends App
The NeuralNet_XLTest object is used to test the NeuralNet_XL class.
The NeuralNet_XLTest object is used to test the NeuralNet_XL class. For this test, the initial weights are used for prediction. > runMain scalation.analytics.NeuralNet_XLTest
object NeuralNet_XLTest2 extends App
The NeuralNet_XLTest2 object is used to test the NeuralNet_XL class.
The NeuralNet_XLTest2 object is used to test the NeuralNet_XL class. For this test, training data is used to fit the weights before using them for prediction.

See also
http://www4.rgu.ac.uk/files/chapter3%20-%20bp.pdf > runMain scalation.analytics.NeuralNet_XLTest2
object NonLinRegressionTest extends App
The NonLinRegressionTest object tests the NonLinRegression class: y = f(x; b) = b0 + exp (b1 * x0).
The NonLinRegressionTest object tests the NonLinRegression class: y = f(x; b) = b0 + exp (b1 * x0).

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
object NullModelTest extends App
The NullModelTest object is used to test the NullModel class.
The NullModelTest object is used to test the NullModel class.
y = b dot x + e = b0 + e
> runMain scalation.analytics.NullModelTest
object NullModelTest2 extends App
The NullModelTest2 object is used to test the NullModel class.
The NullModelTest2 object is used to test the NullModel class.
y = b dot x + e = b0 + e
> runMain scalation.analytics.NullModelTest2
object PerceptronTest extends App
The PerceptronTest object is used to test the Perceptron class.
The PerceptronTest object is used to test the Perceptron class. For this test, training data is used to fit the weights before using them for prediction.

See also
www4.rgu.ac.uk/files/chapter3%20-%20bp.pdf > runMain scalation.analytics.PerceptronTest
object PerceptronTest2 extends App
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 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 regression equation is the following:
y = sigmoid (w dot x) = sigmoid (w0 + w1*x1 + w2*x2 + w3*x3)
> runMain scalation.analytics.PerceptronTest2
object PoissonRegression
object PoissonRegressionTest extends App
The PoissonRegression object tests the PoissonRegression class.
The PoissonRegression object tests the PoissonRegression class.

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
object PoissonRegressionTest2 extends App
The PoissonRegressionTest2 object tests the PoissonRegression class.
The PoissonRegressionTest2 object tests the PoissonRegression class.

See also
www.stat.wisc.edu/~mchung/teaching/.../GLM.logistic.Rpackage.pdf
statmaster.sdu.dk/courses/st111/module03/index.html
object PolyRegressionTest extends App
The PolyRegressionTest object tests PolyRegression class using the following regression equation.
The PolyRegressionTest object tests PolyRegression class using the following regression equation.
y = b dot x = b_0 + b_1*t + b_2*t^2 + ... b_k*t_k
Note, the 'order' at which R-Squared drops is QR(7), Cholesky(14), SVD(6), Inverse(13). > runMain scalation.analytics.PolyRegressionTest
object PolyRegressionTest2 extends App
The PolyRegressionTest2 object tests PolyRegression class using the following regression equation.
The PolyRegressionTest2 object tests PolyRegression class using the following regression equation. This version uses orthogonal polynomials.
y = b dot x = b_0 + b_1*t + b_2*t^2 + ... b_k*t_k
> runMain scalation.analytics.PolyRegressionTest2
object PredictorTest extends App
The PredictorTest object tests all the classes in the scalation.analytics package that directly or indirectly extend the Predictor trait.
The PredictorTest object tests all the classes in the scalation.analytics package that directly or indirectly extend the Predictor trait. FIX - make first test uniform so that the modeling techniques may be compared > runMain scalation.analytics.PredictorTest
object PrincipalComponentsTest extends App
The PrincipalComponentsTest object is used to test the PrincipalComponents class.
The PrincipalComponentsTest object is used to test the PrincipalComponents class.

See also
www.ce.yildiz.edu.tr/personal/songul/file/1097/principal_components.pdf > runMain scalation.analytics.PrincipalComponentsTest
object Probability extends Error
The Probability object provides methods for operating on univariate and bivariate probability distributions of discrete random variables 'X' and 'Y'.
The Probability object provides methods for operating on univariate and bivariate probability distributions of discrete random variables 'X' and 'Y'. A probability distribution is specified by its probability mass functions (pmf) stored either as a "probability vector" for a univariate distribution or a "probability matrix" for a bivariate distribution.
joint probability matrix: pxy(i, j) = P(X = x_i, Y = y_j) marginal probability vector: px(i) = P(X = x_i) conditional probability matrix: px_y(i, j) = P(X = x_i|Y = y_j)
In addition to computing joint, marginal and conditional probabilities, methods for computing entropy and mutual information are also provided. Entropy provides a measure of disorder or randomness. If there is little randomness, entropy will close to 0, while when randomness is high, entropy will be close to, e.g., 'log2 (px.dim)'. Mutual information provides a robust measure of dependency between random variables (contrast with correlation).

See also
scalation.stat.StatVector
object ProbabilityTest extends App
The ProbabilityTest object is used to test the Probability object.
object ProbabilityTest2 extends App
The ProbabilityTest2 provides upper bound for 'entropy' and 'entropy_k'.
object QuadraticFitTest extends App
The QuadraticFitTest object is used to test the QuadraticFit class for a two dimensional case.
object QuadraticFitTest2 extends App
The QuadraticFitTest2 object is used to test the QuadraticFit class for a three dimensional case.
object QuadraticFitTest3 extends App
The QuadraticFitTest3 object is used to test the QuadraticFit class for a three dimensional case with noise.
object RegTechnique extends Enumeration
The RegTechnique object defines the implementation techniques available.
object Regression
The Regression companion object provides a testing method.
object RegressionTest extends App
The RegressionTest object tests Regression class using the following regression equation.
The RegressionTest object tests Regression class using the following regression equation.
y = b dot x = b_0 + b_1*x_1 + b_2*x_2.

See also
statmaster.sdu.dk/courses/st111/module03/index.html > runMain scalation.analytics.RegressionTest
object RegressionTest2 extends App
The RegressionTest2 object tests Regression class using the following regression equation.
The RegressionTest2 object tests Regression class using the following regression equation.
y = b dot x = b_0 + b_1*x1 + b_2*x_2.
> runMain scalation.analytics.RegressionTest2
object RegressionTest3 extends App
The RegressionTest3 object tests the multi-collinearity method in the Regression class using the following regression equation.
The RegressionTest3 object tests the multi-collinearity method in the Regression class using the following regression equation.
y = b dot x = b_0 + b_1*x_1 + b_2*x_2 + b_3*x_3 + b_4 * x_4

See also
online.stat.psu.edu/online/development/stat501/data/bloodpress.txt > runMain scalation.analytics.RegressionTest3
online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html
object RegressionTest4 extends App
The RegressionTest4 object tests the multi-collinearity method in the Regression class using the following regression equation.
The RegressionTest4 object tests the multi-collinearity method in the Regression class using the following regression equation.
y = b dot x = b_0 + b_1*x_1 + b_2*x_2 + b_3*x_3 + b_4 * x_4

See also
online.stat.psu.edu/online/development/stat501/data/bloodpress.txt > runMain scalation.analytics.RegressionTest4
online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html
object RegressionTest5 extends App
The RegressionTest5 object tests Regression class using the following regression equation.
The RegressionTest5 object tests Regression class using the following regression equation.
y = b dot x = b_0 + b_1*x1 + b_2*x_2.
> runMain scalation.analytics.RegressionTest5
object Regression_WLS
The Regression_WLS companion object provides methods for setting weights and testing.
object Regression_WLSTest extends App
The Regression_WLSTest object tests Regression_WLS class using the following regression equation.
The Regression_WLSTest object tests Regression_WLS class using the following regression equation.
y = b dot x = b_0 + b_1*x_1 + b_2*x_2.

See also
statmaster.sdu.dk/courses/st111/module03/index.html > runMain scalation.analytics.Regression_WLSTest
object ResponseSurface
The ResponseSurface companion object provides methods for creating functional forms.
object ResponseSurfaceTest extends App
The ResponseSurfaceTest object is used to test the ResponseSurface class.
The ResponseSurfaceTest object is used to test the ResponseSurface class. > runMain scalation.analytics.ResponseSurfaceTest
object RidgeRegressionTest extends App
The RidgeRegressionTest object tests RidgeRegression class using the following regression equation.
The RidgeRegressionTest object tests RidgeRegression class using the following regression equation.
y = b dot x = b_1*x_1 + b_2*x_2.
Test regression and backward elimination.

See also
http://statmaster.sdu.dk/courses/st111/module03/index.html
object RidgeRegressionTest2 extends App
The RidgeRegressionTest2 object tests RidgeRegression class using the following regression equation.
The RidgeRegressionTest2 object tests RidgeRegression class using the following regression equation.
y = b dot x = b_1*x1 + b_2*x_2.
object RidgeRegressionTest3 extends App
The RidgeRegressionTest3 object tests the multi-collinearity method in the RidgeRegression class using the following regression equation.
The RidgeRegressionTest3 object tests the multi-collinearity method in the RidgeRegression class using the following regression equation.
y = b dot x = b_1*x_1 + b_2*x_2 + b_3*x_3 + b_4 * x_4

See also
online.stat.psu.edu/online/development/stat501/data/bloodpress.txt
online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html
object SimpleRegression
The SimpleRegression companion object provides a simple factory method for building simple regression linear regression models.
object SimpleRegressionTest extends App
The SimpleRegressionTest object to test the SimpleRegression class:
The SimpleRegressionTest object to test the SimpleRegression class:
y = b0 + b1 * x
> runMain scalation.analytics.SimpleRegressionTest
object SimpleRegressionTest2 extends App
The SimpleRegressionTest2 object is used to test the SimpleRegression class.
The SimpleRegressionTest2 object is used to test the SimpleRegression class.
y = b dot x = [b0, b1] dot [1, x1]

See also
http://www.analyzemath.com/statistics/linear_regression.html > runMain scalation.analytics.SimpleRegressionTest2
object SimpleRegressionTest3 extends App
The SimpleRegressionTest3 object is used to test the SimpleRegression class
The SimpleRegressionTest3 object is used to test the SimpleRegression class
y = b dot x = b0 + b1 * x1

See also
http://mathbits.com/mathbits/tisection/Statistics2/linear.htm > runMain scalation.analytics.SimpleRegressionTest3
object SimpleTest extends App
object SimplerRegression
The SimplerRegression companion object provides a simple factory method for building simple regression linear regression models.
object SimplerRegressionTest extends App
The SimplerRegressionTest object is used to test the SimplerRegression class.
The SimplerRegressionTest object is used to test the SimplerRegression class.
y = b0 * x + e
> runMain scalation.analytics.SimplerRegressionTest
object SimplerRegressionTest2 extends App
The SimplerRegressionTest2 object is used to test the SimplerRegression class.
The SimplerRegressionTest2 object is used to test the SimplerRegression class.
y = b dot x + e = [b0] dot [x0] + e
> runMain scalation.analytics.SimplerRegressionTest2
object SimplerRegressionTest3 extends App
The SimplerRegressionTest3 object is used to test the SimplerRegression class.
The SimplerRegressionTest3 object is used to test the SimplerRegression class.
y = b dot x = b0 * x0

See also
http://mathbits.com/mathbits/tisection/Statistics2/linear.htm > runMain scalation.analytics.SimplerRegressionTest3
object TranRegression
The TranRegression companion object provides transformation and inverse transformation function based on the parameter 'lambda'.
The TranRegression companion object provides transformation and inverse transformation function based on the parameter 'lambda'. It support the family of Box-Cox transformations.
object TranRegressionTest extends App
The TranRegressionTest object tests TranRegression class using the following regression equation.
The TranRegressionTest object tests TranRegression class using the following regression equation.
log (y) = b dot x = b_0 + b_1*x_1 + b_2*x_2.
> runMain scalation.analytics.TranRegressionTest
object TranRegressionTest2 extends App
The TranRegressionTest2 object tests TranRegression class using the following regression equation.
The TranRegressionTest2 object tests TranRegression class using the following regression equation.
sqrt (y) = b dot x = b_0 + b_1*x_1 + b_2*x_2.
> runMain scalation.analytics.TranRegressionTest2
object TrigRegressionTest extends App
The TrigRegressionTest object tests TrigRegression class using the following regression equation.
The TrigRegressionTest object 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.analytics.TrigRegressionTest
object TrigRegressionTest2 extends App
The TrigRegressionTest2 object tests TrigRegression class using the following regression equation.
The TrigRegressionTest2 object 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.analytics.TrigRegressionTest2

Packages

analytics

package analytics

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Packages

analytics 

package analytics

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analytics