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 fit the parameter vector
b = x_pinv * y
where 'x_pinv' is the pseudo-inverse.

See also
see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
class ANOVA extends Predictor with Error
The ANOVA class supports one-way ANalysis Of VAriance (ANOVA).
The ANOVA class supports one-way ANalysis Of VAriance (ANOVA). 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 fit the parameter vector
b = x_pinv * y
where 'x_pinv' is the pseudo-inverse.

See also
psych.colorado.edu/~carey/Courses/PSYC5741/handouts/GLM%20Theory.pdf
class ARIMA extends Predictor with Error
The ARIMA class provides basic time series analysis capabilities for Auto- Regressive 'AR' Integrated 'I' Moving-Average 'MA' models.
The ARIMA class provides basic time series analysis capabilities for Auto- Regressive 'AR' Integrated 'I' Moving-Average 'MA' models. In an 'ARIMA(p, d, q)' model, 'p' and 'q' refer to the order of the Auto-Regressive and Moving-Average components of the model; 'd' refers to the order of differencing. ARIMA models are often used for forecasting. Given time series data stored in vector 'y', its next value 'y_t = y(t)' may be predicted based on prior values of 'y' and its noise:
y_t = c + Σ(φ_i y_t-i) + Σ(θ_i e_t-i) + e_t
where 'c' is a constant, 'φ' is the autoregressive coefficient vector, 'θ' is the moving-average coefficient vector, and 'e' is the noise vector. If 'd' > 0, then the time series must be differenced first before applying the above model. ------------------------------------------------------------------------------
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 Predictor with Error
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 ExpSmoothing extends Predictor with Error
The ExpSmoothing class provide very basic time series analysis capabilities of Exponential Smoothing models.
The ExpSmoothing class provide very basic time series analysis capabilities of Exponential Smoothing models. ExpSmoothing models are often used for forecasting. Given time series data stored in vector 'y', its next value 'y_t = y(t)' may be predicted based on prior/smoothed values of 'y':
y_t = s_t-1 + α (s_t-1 - s_t-2)
where vector 's' is the smoothed version of vector 'y' and 'α in [0, 1]' is the smoothing parameter. ------------------------------------------------------------------------------
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, ANOVA - GLM form of ANalysis Of VAriance, ANCOVA - GLM form of ANalysis of COVAriance.
class KalmanFilter extends AnyRef
The KalmanFilter class is used to fit state-space models.
The KalmanFilter class is used to fit state-space models.

See also
en.wikipedia.org/wiki/Kalman_filter FIX: needs more thorough testing
class LassoRegression [MatT <: MatriD, VecT <: VectoD] extends Predictor with Error
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). Use Least-Squares (minimizing the residuals) to fit the parameter vector
b = x_pinv * y [ alternative: b = solve (y) ]
where 'x_pinv' is the pseudo-inverse. Three techniques are provided:
'QR' // QR Factorization: slower, more stable (default) 'Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)

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
class NeuralNet extends Predictor with Error
The NeuralNet class supports basic 3-layer (input, hidden and output) Neural Networks.
The NeuralNet 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 Predictor with Error
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 Perceptron extends Predictor with Error
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 Predictor with Error
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 Predictor with Error
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 fit the parameter vector
b = x_pinv * y
where 'x_pinv' is the pseudo-inverse.

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.
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 [MatT <: MatriD, VecT <: VectoD] extends Predictor with Error
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 fit the parameter vector
b = fac.solve (.)
Four 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 [MatT <: MatriD, VecT <: VectoD] extends Regression[MatriD, VectoD]
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, x_1, ... x_k]. 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 pass to OLS Regression. Four 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 Predictor with Error
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 [MatT <: MatriD, VecT <: VectoD] extends Predictor with Error
The RidgeRegression class supports multiple linear regression.
The RidgeRegression class supports multiple linear regression. In this case, 'x' is multi-dimensional [x_1, ... x_k]. 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 fit the parameter vector
b = fac.solve (.) with regularization x.t * x + λ * I
Four 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 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique

See also
statweb.stanford.edu/~tibs/ElemStatLearn/
class SimpleRegression extends Predictor with Error
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 'x_1', i.e., (1, x_1). Fit the parameter vector 'b' in the regression equation
y = b dot x + e = (b_0, b_1) dot (1, x_1) + e = b_0 + b_1 * x_1 + e
where 'e' represents the residuals (the part not explained by the model).
class SimpleTest [VecT <: VectoD] extends AnyRef
class TranRegression extends Predictor with Error
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: log (y), sqrt (y) when y > 0 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 = x_pinv * y where 'x_pinv' is the pseudo-inverse. Caveat: this class does not provide transformations on columns of matrix 'x'.
class TrigRegression extends Predictor with Error
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 fit the parameter vector
b = x_pinv * y
where 'x_pinv' is the pseudo-inverse.

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
> run-main scalation.analytics.ANCOVATest
object ANOVATest extends App
The ANOVATest object tests the ANOVA class using the following regression equation.
The ANOVATest object tests the ANOVA class using the following regression equation.
y = b dot x = b_0 + b_1*d_1 + b_2*d_2
object ARIMATest extends App
The ARIMATest object is used to test the ARIMA class.
The ARIMATest object is used to test the ARIMA class. > run-main scalation.analytics.ARIMATest
object ARIMATest2 extends App
The ARIMATest2 object is used to test the ARIMA class.
The ARIMATest2 object is used to test the ARIMA class. > run-main scalation.analytics.ARIMATest2
object ARIMATest3 extends App
The ARIMATest3 object is used to test the ARIMA class.
The ARIMATest3 object is used to test the ARIMA class. Forecasting lake levels.

See also
??? > run-main scalation.analytics.ARIMATest3
object ARIMATest4 extends App
The ARIMATest4 object is used to test the ARIMA class.
The ARIMATest4 object is used to test the ARIMA class. > run-main scalation.analytics.ARIMATest4
object ActivationFunc
The ActivationFunc object contains common Activation functions.
The ActivationFunc object contains common Activation functions.

See also
en.wikipedia.org/wiki/Activation_function
object Centering
The Centering object is used to center the input matrix 'x'.
The Centering object is used to center the input matrix 'x'. This is done by subtracting the column means from each value.
object ExpRegressionTest extends App
The ExpRegressionTest object tests ExpRegression class using the following exponential regression problem.
object ExpRegressionTest2 extends App
The ExpRegressionTest2 object has a basic test for the ExpRegression class.
object ExpSmoothingTest extends App
The ExpSmoothingTest object is used to test the ExpSmoothing class.
The ExpSmoothingTest object is used to test the ExpSmoothing class. > run-main scalation.analytics.ExpSmoothingTest
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, 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 KalmanFilterTest extends App
The KalmanFilterTest object is used to test the KalmanFilter class.
The KalmanFilterTest object is used to test the KalmanFilter class.

See also
en.wikipedia.org/wiki/Kalman_filter > run-main scalation.analytics.KalmanFilterTest
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.
Test regression and backward elimination.

See also
http://statmaster.sdu.dk/courses/st111/module03/index.html > run-main scalation.analytics.LassoRegressionTest
object NMFactorizationTest extends App
The NMFactorizationTest object to test NMFactorizationTest class.
object NeuralNetTest extends App
The NeuralNetTest object is used to test the NeuralNet class.
The NeuralNetTest object is used to test the NeuralNet class. For this test, the initial weights are used for used for prediction.
object NeuralNetTest2 extends App
The NeuralNetTest2 object is used to test the NeuralNet class.
The NeuralNetTest2 object is used to test the NeuralNet 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
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 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, the initial weights are used for used for prediction. > run-main scalation.analytics.PerceptronTest
object PerceptronTest2 extends App
The PerceptronTest2 object is used to test the Perceptron class.
The PerceptronTest2 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 > run-main scalation.analytics.PerceptronTest
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.
Note, the 'order' at which R-Squared drops is QR(7), Cholesky(14), SVD(6), Inverse(13). > run-main scalation.analytics.PolyRegressionTest
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. > run-main scalation.analytics.PredictorTet
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 > run-main 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.
Test regression and backward elimination.

See also
statmaster.sdu.dk/courses/st111/module03/index.html > run-main 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.
Test regression using QR Decomposition and Gaussian Elimination for computing the pseudo-inverse. > run-main 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 > run-main 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 > run-main scalation.analytics.RegressionTest4
online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html
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.
Test regression and backward elimination.

See also
statmaster.sdu.dk/courses/st111/module03/index.html > run-main scalation.analytics.Regression_WLSTest
object ResponseSurfaceTest extends App
The ResponseSurfaceTest object is used to test the ResponseSurface class.
The ResponseSurfaceTest object is used to test the ResponseSurface class. > run-main 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.
Test regression using QR Decomposition and Gaussian Elimination for computing the pseudo-inverse.
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
> run-main scalation.analytics.SimpleRegressionTest
object SimpleRegressionTest2 extends App
The SimpleRegressionTest2 object to test the SimpleRegression class:
The SimpleRegressionTest2 object to test the SimpleRegression class:
y = b dot x = (b_0, b_1) dot (1, x_1).

See also
http://www.analyzemath.com/statistics/linear_regression.html > run-main scalation.analytics.SimpleRegressionTest2
object SimpleRegressionTest3 extends App
The SimpleRegressionTest3 object to test the SimpleRegression class:
The SimpleRegressionTest3 object to test the SimpleRegression class:
y = b dot x = b_0 + b_1*x_1.

See also
http://mathbits.com/mathbits/tisection/Statistics2/linear.htm > run-main scalation.analytics.SimpleRegressionTest3
object SimpleTest extends App
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.
> run-main scalation.analytics.TranRegressionTest
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*t + b_2*t^2.
> run-main scalation.analytics.TrigRegressionTest

Packages

analytics

package analytics

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Packages

analytics 

package analytics

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analytics