scalation.modeling

package scalation.modeling

Members list

Packages

Type members

Classlikes

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

Attributes

See also: en.wikipedia.org/wiki/Activation_function Convention: fun activation function (e.g., sigmoid) fun_ vector version of activation function (e.g., sigmoid_) funD vector version of dervivative (e.g., sigmoidD)

Supports: id, reLU, lreLU, eLU, tanh, sigmoid, gaussian, softmax Related functions: logistic, logit
Supertypes: class Object

trait Matchable

class Any
Self type: ActivationFun.type

The BestStep is used to record the best improvement step found so far during feature selection. Note, best depends on whether maximizing or minimizing

Value parameters

bestq: the best QoF for metric qk so far
col: the column/variable to ADD/REMOVE for this step
mod: the model including selected features/variables for this step
mod_cols: the columns selected for mod
qk: the index for the Quality of Fit (QoF) measure/metric used for comparison
qof: the Quality of Fit (QoF) for this step

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait Ordered[BestStep]

trait Comparable[BestStep]

class Object

trait Matchable

class Any
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The BridgeRegression class supports L0.5 Regularization (Bridge Regression with q = 0.5) using Iterative Re-weighted Least Squares (IRLS) to handle non-convex L0.5 penalty.

Value parameters

fname_: feature names
hparam: hyper-parameters: "lambda" (penalty), "maxIter", "tol", "eps"
x: the centered data/input m-by-n matrix
xℱ: the transformation applied to x (e.g., Center or Norm)
y: the centered response/output m-vector
yℱ: the transformation applied to y (e.g., Center)

Attributes

Companion: object
Supertypes: trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
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The BridgeRegression companion object defines hyper-parameters and factory methods.

Attributes

Companion: class
Supertypes: trait Regularized

class Object

trait Matchable

class Any
Self type: BridgeRegression.type

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: DistanceOutlier.type

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: Example_AutoMPG.type

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: Example_BPressure.type

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: Example_BasketBall.type

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: www.stat.uni-muenchen.de/~leiten/Lehre/Material/GLM_0708/chapterGLM.pdf
Companion: object
Supertypes: trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

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

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: ExpRegression.type

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: class RegressionCat

The FeatureSelection trait establishes a framework for feature selection, i.e., selecting the features (e.g., variable x_j, cross term x_j x_k, or functional form x_j^2) to include in the model.

Attributes

Companion: object
Supertypes: class Object

trait Matchable

class Any
Known subtypes: trait Classifier

class BaggingTrees

class RandomForest

class DecisionTree_C45

class DecisionTree_C45wp

class DecisionTree_ID3

class DecisionTree_ID3wp

class HiddenMarkov

class KNN_Classifier

class LinDiscAnalyis

class NaiveBayes

class NaiveBayesR

class NullModel

class SimpleLDA

class SimpleLogisticRegression

class LogisticRegression

class SupportVectorMachine

class TANBayes

class NeuralNet_2L_Ck

class NeuralNet_3L_C2

class Forecaster_RegV

class VAR

class VARX

class Forecaster_Reg

class ARX

class ARX_Quad

class ARX_SR

class ARY

class ARY_Quad

class SARY

trait PredictorMV

class CNN_1D

class NeuralNet_2L

class NeuralNet_3L

class NeuralNet_XL

class NeuralNet_XLT

class RegressionMV

class RidgeRegressionMV

trait Predictor

class ClusteringPredictor

class ELM_3L1

class RegressionTree

class RegressionTreeGB

class RegressionTreeGB4TS

class RegressionTreeMT

class RegressionTreeMT4TS

class RegressionTreeRF

class RegressionTreeRF4TS

class RegressionTreeRF_MT4TS

class RegressionTreeRF_MT

class BridgeRegression

class ExpRegression

class KNN_Regression

class LassoRegression

class SymLassoRegression

class NonlinearRegression

class NullModel

class Perceptron

class PoissonRegression

class QuantileReg

class Regression

class PolyORegression

class PolyRegression

class RegressionCat

class RegressionWLS

class RoundRegression

class SymbolicRegression

class TranRegression

class TranRegression2

class TrigRegression

class RidgeBridgeRegression

class RidgeRegression

class SymRidgeRegression

class SimpleExpRegression

class SimpleRegression

class SimplerRegression
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The FeatureSelection object provides getter/setter methods for determining whether FS works with the FULL DATASET or just the TRAINING SET.

Attributes

Companion: trait
Supertypes: class Object

trait Matchable

class Any
Self type: FeatureSelection.type

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

Value parameters

df: the degrees of freedom for error
dfr: the degrees of freedom for regression/model

Attributes

See also: reset to reset the degrees of freedom
Companion: object
Supertypes: trait FitM

class Object

trait Matchable

class Any
Known subtypes: class ClusteringPredictor

class Diagnoser

class AR_Star

class Forecaster_RegV

class VAR

class VARX

class RandomWalk_Star

class Forecaster

class AR

class ARMA

class Forecaster_D

class NeuralNet_3L4TS

class ARX_D

class NARX_SR_D

class ARX_Quad_D

class ARX_SR_D

class ARY_D

class Forecaster_Reg

class ARX

class ARX_Quad

class ARX_SR

class ARY

class ARY_Quad

class SARY

class NullModel

class RandomWalk

class RandomWalkS

class SimpleExpSmoothing

class SimpleMovingAverage

class WeightedMovingAverage

class SimpleMovingAverage2

class TrendModel

class CNN_1D

class CNN_2D

class ELM_3L1

class NeuralNet_2L

class NeuralNet_3L

class NeuralNet_XL

class NeuralNet_XLT

class RegressionMV

class RidgeRegressionMV

class RegressionTree

class RegressionTreeGB

class RegressionTreeGB4TS

class RegressionTreeMT

class RegressionTreeMT4TS

class RegressionTreeRF

class RegressionTreeRF4TS

class RegressionTreeRF_MT4TS

class RegressionTreeRF_MT

class BridgeRegression

class ExpRegression

class KNN_Regression

class LassoRegression

class SymLassoRegression

class NonlinearRegression

class NullModel

class Perceptron

class PoissonRegression

class QuantileReg

class Regression

class PolyORegression

class PolyRegression

class RegressionCat

class RegressionWLS

class RoundRegression

class SymbolicRegression

class TranRegression

class TranRegression2

class TrigRegression

class RidgeBridgeRegression

class RidgeRegression

class SymRidgeRegression

class SimpleExpRegression

class SimpleRegression

class SimplerRegression

class TestFit
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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

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

The FitM trait 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

See also: Fit for a more complete implementation suitable for several models.
Companion: object
Supertypes: class Object

trait Matchable

class Any
Known subtypes: trait FitC

class BaggingTrees

class RandomForest

class DecisionTree_C45

class DecisionTree_C45wp

class DecisionTree_ID3

class DecisionTree_ID3wp

class HiddenMarkov

class KNN_Classifier

class LinDiscAnalyis

class NaiveBayes

class NaiveBayesR

class NullModel

class SimpleLDA

class SimpleLogisticRegression

class LogisticRegression

class SupportVectorMachine

class TANBayes

class NeuralNet_2L_Ck

class NeuralNet_3L_C2

class RNN

class Baseline

trait Fit

class ClusteringPredictor

class Diagnoser

class AR_Star

class Forecaster_RegV

class VAR

class VARX

class RandomWalk_Star

class Forecaster

class AR

class ARMA

class Forecaster_D

class NeuralNet_3L4TS

class ARX_D

class NARX_SR_D

class ARX_Quad_D

class ARX_SR_D

class ARY_D

class Forecaster_Reg

class ARX

class ARX_Quad

class ARX_SR

class ARY

class ARY_Quad

class SARY

class NullModel

class RandomWalk

class RandomWalkS

class SimpleExpSmoothing

class SimpleMovingAverage

class WeightedMovingAverage

class SimpleMovingAverage2

class TrendModel

class CNN_1D

class CNN_2D

class ELM_3L1

class NeuralNet_2L

class NeuralNet_3L

class NeuralNet_XL

class NeuralNet_XLT

class RegressionMV

class RidgeRegressionMV

class RegressionTree

class RegressionTreeGB

class RegressionTreeGB4TS

class RegressionTreeMT

class RegressionTreeMT4TS

class RegressionTreeRF

class RegressionTreeRF4TS

class RegressionTreeRF_MT4TS

class RegressionTreeRF_MT

class BridgeRegression

class ExpRegression

class KNN_Regression

class LassoRegression

class SymLassoRegression

class NonlinearRegression

class NullModel

class Perceptron

class PoissonRegression

class QuantileReg

class Regression

class PolyORegression

class PolyRegression

class RegressionCat

class RegressionWLS

class RoundRegression

class SymbolicRegression

class TranRegression

class TranRegression2

class TrigRegression

class RidgeBridgeRegression

class RidgeRegression

class SymRidgeRegression

class SimpleExpRegression

class SimpleRegression

class SimplerRegression

class TestFit
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The Imputation trait specifies an imputation operation called impute to be defined by the objects implementing it, i.e., ImputeMICE - impute missing values using MICE ImputeMRegression - impute missing values using Regression (RI) ImputeSRegression - 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 using the filtered mean ImputeMedian - impute missing values using the filtered median 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 ImputeBackward

object ImputeForward

object ImputeMICE

object ImputeMRegression

object ImputeMean

object ImputeMedian

object ImputeMovingAvg

object ImputeNormal

object ImputeNormalWin

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

Attributes

Supertypes: trait Imputation

class Object

trait Matchable

class Any
Self type: ImputeBackward.type

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

Attributes

Supertypes: trait Imputation

class Object

trait Matchable

class Any
Self type: ImputeForward.type

The ImputeMICE object imputes missing values using MICE. Use the columns in matrix z to impute values for target vector x.

Attributes

Supertypes: trait Imputation

class Object

trait Matchable

class Any
Self type: ImputeMICE.type

The ImputeMRegression object imputes missing values using multiple Regression. Use the columns in matrix z to impute values for target vector x.

Attributes

Supertypes: trait Imputation

class Object

trait Matchable

class Any
Self type: ImputeMRegression.type

The ImputeMean object imputes missing values using the filtered mean.

Attributes

Supertypes: trait Imputation

class Object

trait Matchable

class Any
Self type: ImputeMean.type

The ImputeMean object imputes missing values using the filtered median.

Attributes

Supertypes: trait Imputation

class Object

trait Matchable

class Any
Self type: ImputeMedian.type

The ImputeMovingAvg object imputes missing values using the moving average.

Attributes

Supertypes: trait Imputation

class Object

trait Matchable

class Any
Self type: ImputeMovingAvg.type

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

Attributes

Supertypes: trait Imputation

class Object

trait Matchable

class Any
Self type: ImputeNormal.type

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: ImputeNormalWin.type

The ImputeSRegression object imputes missing values using SimpleRegression.

Attributes

Supertypes: trait Imputation

class Object

trait Matchable

class Any
Self type: ImputeSRegression.type

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: Initializer.type

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 FeatureSelection

trait Model

class Object

trait Matchable

class Any
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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: KNN_Regression.type

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

Attributes

Companion: class
Supertypes: trait Regularized

class Object

trait Matchable

class Any
Self type: LassoRegression.type

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
xℱ: the transformation applied to x (e.g., Center or Norm)
y: the response/output m-vector
yℱ: the transformation applied to y (e.g., Center)

Attributes

See also: see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
Companion: object
Supertypes: trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
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Known subtypes: class SymLassoRegression

The Model companion object provides methods useful for classes extending the Model trait.

Attributes

Companion: trait
Supertypes: class Object

trait Matchable

class Any
Self type: Model.type

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

Companion: object
Supertypes: class Object

trait Matchable

class Any
Known subtypes: trait Classifier

class BaggingTrees

class RandomForest

class DecisionTree_C45

class DecisionTree_C45wp

class DecisionTree_ID3

class DecisionTree_ID3wp

class HiddenMarkov

class KNN_Classifier

class LinDiscAnalyis

class NaiveBayes

class NaiveBayesR

class NullModel

class SimpleLDA

class SimpleLogisticRegression

class LogisticRegression

class SupportVectorMachine

class TANBayes

class NeuralNet_2L_Ck

class NeuralNet_3L_C2

class Forecaster_RegV

class VAR

class VARX

trait ForecasterX

class RegressionTreeGB4TS

class RegressionTreeMT4TS

class RegressionTreeRF4TS

class RegressionTreeRF_MT4TS

trait Forecast

class AR_Star

class RandomWalk_Star

class Forecaster

class AR

class ARMA

class Forecaster_D

class NeuralNet_3L4TS

class ARX_D

class NARX_SR_D

class ARX_Quad_D

class ARX_SR_D

class ARY_D

class Forecaster_Reg

class ARX

class ARX_Quad

class ARX_SR

class ARY

class ARY_Quad

class SARY

class NullModel

class RandomWalk

class RandomWalkS

class SimpleExpSmoothing

class SimpleMovingAverage

class WeightedMovingAverage

class SimpleMovingAverage2

class TrendModel

class CNN_2D

trait PredictorMV

class CNN_1D

class NeuralNet_2L

class NeuralNet_3L

class NeuralNet_XL

class NeuralNet_XLT

class RegressionMV

class RidgeRegressionMV

trait Predictor

class ClusteringPredictor

class ELM_3L1

class RegressionTree

class RegressionTreeGB

class RegressionTreeMT

class RegressionTreeRF

class RegressionTreeRF_MT

class BridgeRegression

class ExpRegression

class KNN_Regression

class LassoRegression

class SymLassoRegression

class NonlinearRegression

class NullModel

class Perceptron

class PoissonRegression

class QuantileReg

class Regression

class PolyORegression

class PolyRegression

class RegressionCat

class RegressionWLS

class RoundRegression

class SymbolicRegression

class TranRegression

class TranRegression2

class TrigRegression

class RidgeBridgeRegression

class RidgeRegression

class SymRidgeRegression

class SimpleExpRegression

class SimpleRegression

class SimplerRegression
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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 Optimizer_Adam

class Optimizer_SGD

class Optimizer_SGDM

class Perceptron

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 ClusteringPredictor

class AR_Star

class RandomWalk_Star

class AR

class NullModel

class RandomWalk

class RandomWalkS

class SimpleExpSmoothing

class SimpleMovingAverage

class WeightedMovingAverage

class SimpleMovingAverage2

class TrendModel

class NonlinearRegression

class NullModel

class SimpleExpRegression

class SimpleRegression

class SimplerRegression
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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: www.bsos.umd.edu/socy/alan/stats/socy602_handouts/kut86916_ch13.pdf
Companion: object
Supertypes: trait NoSubModels

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

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

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: NonlinearRegression.type

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

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 FeatureSelection

trait Model

class Object

trait Matchable

class Any
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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: object DistanceOutlier

object QuantileOutlier

object QuartileXOutlier

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 FeatureSelection

trait Model

class Object

trait Matchable

class Any
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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

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 FeatureSelection

trait Model

class Object

trait Matchable

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

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: PoissonRegression.type

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: www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx
Companion: object
Supertypes: class Regression

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

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: PolyORegression.type

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: www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx
Companion: object
Supertypes: class Regression

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

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: PolyRegression.type

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 FeatureSelection

trait Model

class Object

trait Matchable

class Any
Known subtypes: class ClusteringPredictor

class ELM_3L1

class RegressionTree

class RegressionTreeGB

class RegressionTreeGB4TS

class RegressionTreeMT

class RegressionTreeMT4TS

class RegressionTreeRF

class RegressionTreeRF4TS

class RegressionTreeRF_MT4TS

class RegressionTreeRF_MT

class BridgeRegression

class ExpRegression

class KNN_Regression

class LassoRegression

class SymLassoRegression

class NonlinearRegression

class NullModel

class Perceptron

class PoissonRegression

class QuantileReg

class Regression

class PolyORegression

class PolyRegression

class RegressionCat

class RegressionWLS

class RoundRegression

class SymbolicRegression

class TranRegression

class TranRegression2

class TrigRegression

class RidgeBridgeRegression

class RidgeRegression

class SymRidgeRegression

class SimpleExpRegression

class SimpleRegression

class SimplerRegression
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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

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

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: QuantileOutlier.type

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: QuantileReg.type

The QuantileReg class supports quantile regression.

Value parameters

fname_: the feature/variable names (defaults to null)
hparam: the hyper-parameters (defaults to QuantileReg.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

Companion: object
Supertypes: trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

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: QuartileXOutlier.type

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.

en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)
Companion: object
Supertypes: trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all
Known subtypes: class PolyORegression

class PolyRegression

class RegressionCat

class RegressionWLS

class RoundRegression

class SymbolicRegression

class TranRegression

class TranRegression2

class TrigRegression
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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

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: trait ExpandableVariable

class Regression

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

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

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: RegressionCat.type

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

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: RegressionWLS.type

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

www.markirwin.net/stat149/Lecture/Lecture3.pdf
Companion: object
Supertypes: class Regression

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

The Regularized trait describes the center method that is to be supported by all companion objects supporting regularized regression.

Attributes

Supertypes: class Object

trait Matchable

class Any
Known subtypes: object BridgeRegression

object LassoRegression

object RidgeBridgeRegression

object RidgeRegression

The RidgeBridgeRegression class supports multiple linear regression with a hybrid of Ridge (L2) and Bridge (Lq with 0 < q < 1) regularization. It solves: y = Xb + e by minimizing: ||y - Xb||^2 + lambda * ||b||^2 + beta * sum(|b_j|^q)

Value parameters

fname_: the feature/variable names (defaults to null)
hparam: the regularization hyper-parameters (lambda for ridge, beta for bridge, q)
x: the centered data/input matrix
xℱ: the transformation applied to x (e.g., Center or Norm)
y: the centered response/output vector
yℱ: the transformation applied to y (e.g., Center)

Attributes

Companion: object
Supertypes: trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

The RidgeBridgeRegression companion object provides default hyper-parameters and convenience factory methods.

Attributes

Companion: class
Supertypes: trait Regularized

class Object

trait Matchable

class Any
Self type: RidgeBridgeRegression.type

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 should be 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
xℱ: the transformation applied to x (e.g., Center or Norm)
y: the centered response/output m-vector
yℱ: the transformation applied to y (e.g., Center)

Attributes

See also: statweb.stanford.edu/~tibs/ElemStatLearn/
Companion: object
Supertypes: trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all
Known subtypes: class SymRidgeRegression

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

Attributes

Companion: class
Supertypes: trait Regularized

class Object

trait Matchable

class Any
Self type: RidgeRegression.type

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

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: RoundRegression.type

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 FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

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 NeuralNet_3L4TS

object CNN_1D

object CNN_2D

object ELM_3L1

object NeuralNet_2L

object NeuralNet_2L_Ck

object NeuralNet_3L

object NeuralNet_3L_C2

object NeuralNet_XL

object NeuralNet_XLT

object Perceptron
Show all

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

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: www.stat.uni-muenchen.de/~leiten/Lehre/Material/GLM_0708/chapterGLM.pdf
Companion: object
Supertypes: trait NoSubModels

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

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: SimpleExpRegression.type

The SimpleNN object contains a simple dataset for testing Gradient Descent (GD) and Incremental Gradient Descent (IGD) optimization algorithms.

Attributes

See also: https://nowak.ece.wisc.edu/MFML.pdf
Supertypes: class Object

trait Matchable

class Any
Self type: SimpleNN.type

The SimpleNN_3L object contains a simple dataset for testing Gradient Descent (GD) and Incremental Gradient Descent (IGD) optimization algorithms.

Attributes

See also: https://nowak.ece.wisc.edu/MFML.pdf
Supertypes: class Object

trait Matchable

class Any
Self type: SimpleNN_3L.type

The SimpleNN object contains a simple dataset for testing Gradient Descent (GD) and Incremental Gradient Descent (IGD) optimization algorithms.

Attributes

See also: https://nowak.ece.wisc.edu/MFML.pdf
Supertypes: class Object

trait Matchable

class Any
Self type: SimplePerceptron.type

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: SimpleRegression.type

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 FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

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 FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

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: SimplerRegression.type

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

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

The SymLassoRegression object provides factory methods.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: SymLassoRegression.type

The SymLassoRegression class 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.

Value parameters

fname: the feature/variable names
hparam: the hyper-parameters (use Regression.hp for default)
powers: the set of powers to raise matrix x to
x: the initial data/input m-by-n matrix (before expansion) must not include an intercept column of all ones
y: the response/output m-vector

Attributes

Companion: object
Supertypes: class LassoRegression

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

The SymRidgeRegression class 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.

Value parameters

fname: the feature/variable names
hparam: the hyper-parameters (use Regression.hp for default)
powers: the set of powers to raise matrix x to
xx: the expanded data/input m-by-n matrix
y: the response/output m-vector

Attributes

Companion: object
Supertypes: class RidgeRegression

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

The SymRidgeRegression object provides several factory methods.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: SymRidgeRegression.type

The SymbolicRegression object provides several factory methods.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: SymbolicRegression.type

The SymbolicRegression class supports a limited form of 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).

Value parameters

fname: the feature/variable names
hparam: the hyper-parameters (use Regression.hp for default)
powers: the set of powers to raise matrix x to
rpowers: the set of rational powers to raise matrix x to (allows a negative base) DON'T use the same powers for powers and rpowers
xx: the expanded data/input m-by-n matrix
y: the response/output m-vector

Attributes

Companion: object
Supertypes: class Regression

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

The TaskType enum specifies the types of tasks supported by ScalaTion.

Value parameters

base: the base trait/abstract class for the given type of task
name: the name of task type

Attributes

Supertypes: trait Enum

trait Serializable

trait Product

trait Equals

class Object

trait Matchable

class Any
Show all

The TestFit class can be used for comparing two vectors on the basis of QoF. The degrees of freedom (dfr) 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

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 tran (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 'tran' is the function (defaults to log1p) 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)
x: the data/input m-by-n matrix
y: the un-transformed response/output m-vector
yℱ: the transformation (f with inverse fi) applied to y (e.g., Boxcox)

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'.

www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx
Companion: object
Supertypes: class Regression

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

The TranRegression companion object provides transformation and inverse transformation function based on the parameter λ. It support the family of Box-Cox and Yeo-Johnson Transformations.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: TranRegression.type

The TranRegression2 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 tran (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 'tran' is the function (defaults to log1p) 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 expm1)
tran: the transformation function (defaults to log1p)
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'.

www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx
Companion: object
Supertypes: class Regression

trait Fit

trait FitM

trait Predictor

trait FeatureSelection

trait Model

class Object

trait Matchable

class Any
Show all

The TranRegression2 companion object provides transformation and inverse transformation function based on the parameter λ. It support the family of Box-Cox and Yeo-Johnson Transformations.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: TranRegression2.type

The TranRegression2Ex 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: TranRegression2Ex.type

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

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

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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

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 FeatureSelection

trait Model

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Types

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

Attributes

Value members

Concrete methods

The activationFunTest main function tests the ActivationFun object. This test individually plots the vector versions of the activation functions f_(t).

runMain scalation.modeling.activationFunTest

Attributes

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

runMain scalation.modeling.activationFunTest2

Attributes

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

runMain scalation.modeling.activationFunTest2

Attributes

The activationFunTest4 main function tests the ActivationFun object softmax activation function.

Attributes

See also: en.wikipedia.org/wiki/Softmax_function

runMain scalation.modeling.activationFunTest4

The activationFunTest5 main function tests the ActivationFun object. It tests the logit_ and logistic_ functions.

runMain scalation.modeling.activationFunTest5

Attributes

The activationFunTest6 main function tests the ActivationFun object. It tests the matricise or matrixize functions.

runMain scalation.modeling.activationFunTest6

Attributes

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

Attributes

See also: statmaster.sdu.dk/courses/st111/module03/index.html

runMain scalation.modeling.bridgeRegressionTest

The bridgeRegressionTest2 main function tests the BridgeRegression class on the AutoMPG dataset.

runMain scalation.modeling.bridgeRegressionTest2

Attributes

The bridgeRegressionTest3 main function tests the multi-collinearity method in the BridgeRegression class using the following regression equation. y = b dot x = b_1x_1 + b_2x_2 Contour Plots for see, L2 penalty, see + L2 penalty, L1 penalty, sse + L1 penalty L.5 penalty, see _ L.5 penalty

runMain scalation.modeling.bridgeRegressionTest3

Attributes

The bridgeRegressionTest4 main function tests the BridgeRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2

runMain scalation.modeling.bridgeRegressionTest4

Attributes

The bridgeRegressionTest5 main function tests the BridgeRegression 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.bridgeRegressionTest5

Attributes

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

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

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

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

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

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

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

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

The example_AutoMPG_write_csv main function writes the AutoMPG dataset into a CSV file in the DATA director (.../scalation_2.0/data).

Attributes

See also: archive.ics.uci.edu/ml/datasets/Auto+MPG

runMain scalation.modeling.example_AutoMPG_write_csv

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

runMain scalation.modeling.example_BPressureTest

Attributes

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

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

runMain scalation.modeling.example_BasketBallTest

Attributes

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

runMain scalation.modeling.expRegressionTest

Attributes

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

runMain scalation.modeling.expRegressionTest

Attributes

The expRegressionTest3 main function tests the SimpleExpRegression class.

Attributes

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

runMain scalation.modeling.expRegressionTest3

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

Value parameters

x: the vector whose extreme values are sought

Attributes

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

The fitTest main function is used to test the Fit trait on a simulated dataset. It test the diagnose method to get metrics on POINT PREDICTIONS.

runMain scalation.modeling.fitTest

Attributes

The fitTest2 main function is used to test the Fit class on a simulated time series. It test the diagnose_ method to get metrics on PREDICTION INTERVALS.

Attributes

See also: scalation.modeling.forecasting.randomWalkTest3 for another test case

runMain scalation.modeling.fitTest2

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

runMain scalation.modeling.imputationTest

Attributes

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

runMain scalation.modeling.imputationTest2

Attributes

The imputationTest3 main function imputes a missing value for the Texas Temperatures dataset that contains 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.imputationTest3

Attributes

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

runMain scalation.modeling.kNN_RegressionTest

Attributes

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

runMain scalation.modeling.kNN_RegressionTest2

Attributes

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

runMain scalation.modeling.kNN_RegressionTest3

Attributes

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

Attributes

See also: statmaster.sdu.dk/courses/st111/module03/index.html

runMain scalation.modeling.lassoRegressionTest

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

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

The lassoRegressionTest4 main function tests the LassoRegression class using the Covid-19 dataset. It illustrates using the Relation/Table class for reading the data from a .csv file "covid_19_weekly.csv". Assumes no missing values. It also combines feature selection with cross-validation and plots R^2, R^2 bar, sMAPE, and R^2 cv vs. the instance index.

runMain scalation.modeling.lassoRegressionTest4

Attributes

The lassoRegressionTest5 main function tests the LassoRegression 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.lassoRegressionTest5

Attributes

The lassoRegressionTest6 main function tests the LassoRegression class using the COVID dataset. It illustrates using the Table class for reading the' data from a .csv file "auto-mpg.csv". Assumes no missing values. It also uses the 'findLambda' method to search for a shrinkage parameter that roughly mininizes 'sse_cv'.

runMain scalation.modeling.lassoRegressionTest6

Attributes

The lassoRegressionTest7 main function tests the multi-collinearity method in the LassoRegression class using the following regression equation. y = b dot x = b_1x_1 + b_2x_2 Contour Plots for see, L2 penalty, see + L2 penalty, L1 penalty, sse + L1 penalty

runMain scalation.modeling.lassoRegressionTest7

Attributes

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

runMain scalation.modeling.matrixTransformTest

Attributes

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

Return the mean and standard deviation stats for vector x

Value parameters

x: the vector whose stats are sought

Attributes

Make a new restricted array of strings for the feature names based on the selected columns.

Value parameters

cols: the selected columns
fname: the original/full set of feature names

Attributes

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

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

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

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

runMain scalation.modeling.nullModelTest

Attributes

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

runMain scalation.modeling.nullModelTest2

Attributes

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

Value parameters

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

Attributes

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 actual and predicted values.

Value parameters

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

Attributes

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

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

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

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

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

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

runMain scalation.modeling.perceptronTest3

Attributes

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

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

The perceptronTest6 main function tests the basic Perceptron equations with a Gradient Descent algorithm.

runMain scalation.modeling.perceptronTest6

Attributes

Return the Pin Ball Loss based on the difference between y and yp = e

Value parameters

e: the error/residual vector
q: the quantile of interest

Attributes

The poissonRegressionTest main function tests the PoissonRegression class.

Attributes

See also: 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

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

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

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

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

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

The polyRegressionTest3 main function tests the collinearity/correlation of x1, x1^2, x1^3 under centering, standardizing, and min-max normalization, Picking an min-max interval like [-2, 2] or [-3, 3] may make the effect somewhat similar to standardization.

runMain scalation.modeling.polyRegressionTest3

Attributes

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

The quantileRegTest main function tests the QuantileReg class. It tests the Pin Ball Loss Function.

runMain scalation.modeling.quantileRegTest

Attributes

The quantileRegTest2 main function tests a quantile 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 It compare POINT PREDICTIONS of Regression (mean) and QuantileReg (median).

runMain scalation.modeling.quantileRegTest2

Attributes

The quantileRegTest3 main function tests a quantile 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 It compare PREDICTION INTERVALS from Regression and QuantileReg.

runMain scalation.modeling.quantileRegTest3

Attributes

Rectify the prediction/forecast when they are required to be non-negative, by setting negative values to zero.

Value parameters

nneg: whether the values are required to be non-negative (e.g., counts)
yp: the predicted/forecasted value

Attributes

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

The regressionCatTest2 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 This version needs the treatment levels to be shift down to zero.

runMain scalation.modeling.regressionCatTest2

Attributes

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

runMain scalation.modeling.regressionCatTest3

Attributes

The regressionCatTest4 main function tests the RegressionCat class using the AutoMPG dataset. Assumes no missing values. It tests forward, backward and stepwise selection. It makes a Regression model to be compared to RegressionCat in the next test case.

runMain scalation.modeling.regressionCatTest4

Attributes

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

The regressionCatTest6 main function tests the RegressionCat class regarding conflicts between Dummy and Intercept columns (the Dummy Variable Trap). Compare parameters/coefficients for keeping/removing columns in matrix x.

Attributes

See also: www.statlect.com/fundamentals-of-statistics/dummy-variable.

runMain scalation.modeling.regressionCatTest6

The regressionCatTest7 main function tests the RegressionCat class' ability to handle string columns by converting them into dummy variable columns. Note, for larger datasets read from a CSV file using the MatrixD.loadStr method.

Attributes

See also: SymbolicRegression

runMain scalation.modeling.regressionCatTest7

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

The regressionTest10 main function trains a regression model small dataset.

runMain scalation.modeling.regressionTest10

Attributes

The regressionTest11 main function trains a regression model small dataset. val x2 = VectorD (1, 4, 9, 16, 25)

runMain scalation.modeling.regressionTest11

Attributes

The regressionTest12 main function tests the Regression class using the AutoMPG dataset. It illustrates using the Table class for reading the data from a .csv file "auto_mpg.csv". Assumes no missing values. It also combines feature selection with cross-validation and plots R^2, R^2 bar, sMAPE, and R^2 cv vs. the instance index.

runMain scalation.modeling.regressionTest12

Attributes

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

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

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

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

The regressionTest6 main function tests the Regression class using the following regression equation. y = b dot x = b_0 + b_1x_1 + b_2x_2. Show effects of increasing collinearity.

runMain scalation.modeling.regressionTest6

Attributes

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 (x_1), Elevation (x_2) and Longitude (x_3). The model equation is the following: y = b dot x = b_0 + b_1x_1 + b_2x_2 + b_3*x_3

runMain scalation.modeling.regressionTest7

Attributes

The regressionTest8 main function trains a regression model on the Boston House Prices dataset. It illustrates use of the load method in the MatrixD object.

Attributes

See also: scalation.mathstat.MatrixD

runMain scalation.modeling.regressionTest8

The regressionTest9 main function trains a regression model on a simple dataset.

runMain scalation.modeling.regressionTest9

Attributes

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

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

The regressionWLSTest3 main function tests the RegressionWLS class using the AutoMPG dataset. Assumes no missing values. It test cross validation.

runMain scalation.modeling.regressionWLSTest3

Attributes

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

Attributes

See also: statmaster.sdu.dk/courses/st111/module03/index.html

runMain scalation.modeling.ridgeBridgeRegressionTest

The ridgeBridgeRegressionTest2 main function tests the RidgeBridgeRegression 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.ridgeBridgeRegressionTest2

Attributes

The ridgeBridgeRegressionTest3 main function tests the RidgeBridgeRegression 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.ridgeBridgeRegressionTest3

Attributes

The ridgeBridgeRegressionTest4 main function tests the RidgeBridgeRegression class using the following regression equation. y = b dot x = b_1x1 + b_2x_2

runMain scalation.modeling.ridgeBridgeRegressionTest4

Attributes

The ridgeBridgeRegressionTest5 main function tests the RidgeBridgeRegression 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.ridgeBridgeRegressionTest5

Attributes

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

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

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

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

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

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

The ridgeRegressionTest7 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 The determinant of the Gram Matrix X^TX as a measure of linear independence

runMain scalation.modeling.ridgeRegressionTest7

Attributes

The ridgeRegressionTest8 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_2*x_3 Check correlation for perfectly and highly collinear vectors (@see Textbook, exercise 1)

runMain scalation.modeling.ridgeRegressionTest8

Attributes

The ridgeRegressionTest9 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 Contour Plots for see, L2 penalty, see + penalty.

runMain scalation.modeling.ridgeRegressionTest9

Attributes

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

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

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

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

runMain scalation.modeling.simpleExpRegressionTest

Attributes

The SimpleExpRegressionTest2 main function tests the SimpleExpRegression class.

runMain scalation.modeling.simpleExpRegressionTest2

Attributes

The simpleExpRegressionTest3 main function tests the SimpleExpRegression class.

Attributes

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

runMain scalation.modeling.simpleExpRegressionTest3

The simpleNN1 main function illustrates the use of Gradient Descent (GD) to optimize the weights/parameters of a Multiple Linear Regression (MLR) model.

grad g = -x.ᵀ * (y - ŷ)    where pred ŷ = x * b

Computations done at the vector level: X -> y. R^2 = .827

runMain scalation.modeling.simpleNN1

Attributes

The simpleNN2 main function illustrates the use of Incremental Gradient Descent (IGD) to optimize the weights/parameters of a Multiple Linear Regression (MLR) model. Computations done at the vector level: X -> y. R^2 = .933

runMain scalation.modeling.simpleNN2

Attributes

The simpleNN3 main function illustrates the use of Gradient Descent (GD) to optimize the weights/parameters of a simple neural network (Perceptron). Originally, perceptrons used the Heavyside activation function for binary classification problems, but have been extended to multi-class classification and regression problems. Furthermore, when the activation function is identity, the perceptron models are equivalent multiple linear regression models.

grad g = -x.ᵀ * (y - ŷ) * ƒ    where pred ŷ = f(x * b)

Computations done at the vector level: X -> y. R^2 = .865

runMain scalation.modeling.simpleNN3

Attributes

The simpleNN4 main function illustrates the use of Gradient Descent (GD) to optimize the weights/parameters of a simple neural network (2-layer (no hidden) Neural Network).

Prediction Equation: ŷ = f(B^T x) = f(W x + b)

where x is an input vector, ŷ is a predicted output vector, f is the activation function, B is the parameter matrix, W is the weight matrix, and b is the bias vector.

Attributes

The simpleNN5 main function illustrates the use of Gradient Descent (GD) to optimize the weights/parameters of a simple neural network (2-layer (no hidden) Neural Network). Computations done at the matrix level: X -> Y. R^2 = .865, .826

runMain scalation.modeling.simpleNN5

Attributes

The simpleNN6 main function illustrates the use of Gradient Descent (GD) to optimize the weights/parameters of a simple neural network (3-layer (1 hidden) Neural Network). Computations done at the matrix level: X -> Z -> Y. R^2 = .299, .432 (requires more epochs)

runMain scalation.modeling.simpleNN6

Attributes

The simpleNN7 main function illustrates the use of Incremental Gradient Descent (IGD) to optimize the weights/parameters of a simple neural network (3-layer (1 hidden) Neural Network).

Prediction Equation: z = f0(A^T x + α) ŷ = f1(B^T z + β)

where x is an input vector, z is the hidden layer vector, ŷ is a predicted output vector, f0, f1 are the activation functions, A and B are the parameter matrices, and α and β are the bias vectors.

Attributes

The simpleNN8 main function illustrates the use of Incremental Gradient Descent (IGD) to optimize the weights/parameters of a simple neural network (3-layer (1 hidden) Neural Network).

Prediction Equation: z = f0(A^T x + α) ŷ = f1(B^T z + β)

where x is an input vector, z is the hidden layer vector, ŷ is a predicted output vector, f0, f1 are the activation functions, A and B are the parameter matrices, and α and β are the bias vectors. Illustrates the need for RESCALING the data. Computations done at the vector level, x -> z -> y. R^2 = .512 (no rescaling) .813 (rescaling) (for 20 epochs)

runMain scalation.modeling.simpleNN8

Attributes

The simpleNN_3L1 main function illustrates the use of Gradient Descent (GD) to optimize the weights/parameters of a simple (3-layer (1 hidden) Neural Network (NN_3L).

Prediction Equation: z = f0(A^T x + α)
                     ŷ = f1(B^T z + β)

where x is an input matrix, z is the hidden layer matrix, ŷ is a predicted output matrix, f0, f1 are the activation functions, A and B are the parameter matrices, and α and β are the bias vectors. Computations done at the matrix level: X -> Z -> Y. R^2 = .299, .432

runMain scalation.modeling.simpleNN_3L1

Attributes

The simpleNN_3L2 main function illustrates the use of Incremental Gradient Descent (IGD) to optimize the weights/parameters of a simple (3-layer (1 hidden) Neural Network (NN_3L).

Prediction Equation: z = f0(A^T x + α)
                     ŷ = f1(B^T z + β)

where xi is the i-th input vector, z is a hidden layer vector, ŷ is a predicted output vector, f0, f1 are the activation functions, A and B are the parameter matrices, and α and β are the bias vectors.

Attributes

The simplePerceptron1 main function illustrates the use of Gradient Descent (GD) to optimize the weights/parameters of a simple neural network (Perceptron). Originally, perceptrons used the Heavyside activation function for binary classification problems, but have been extended to multi-class classification and regression problems. Furthermore, when the activation function is identity, the perceptron models are equivalent multiple linear regression models.

grad g = -x.ᵀ * (y - ŷ) * ƒ    where pred ŷ = f(x * b)

Computations done at the vector level: X -> y. R^2 = .865

runMain scalation.modeling.simplePerceptron1

Attributes

The simplePerceptron2 main function illustrates the use of Incremental Gradient Descent (IGD) to optimize the weights/parameters of a simple neural network (Perceptron).

grad g = -x.ᵀ * (y - ŷ) * ƒ    where pred ŷ = f(x * b)

Computations done at the scalar level: X -> y. R^2 = .886

runMain scalation.modeling.simplePerceptron2

Attributes

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

runMain scalation.modeling.simpleRegressionTest

Attributes

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

runMain scalation.modeling.simpleRegressionTest2

Attributes

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

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

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

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

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

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

runMain scalation.modeling.simpleRegressionTest8

Attributes

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

runMain scalation.modeling.simplerRegressionTest

Attributes

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

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

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

Shifted Rectified Linear Unit (Shifted ReLU) for a scalar.

Value parameters

a: the slope parameter: a = 1 => _/ , a = -1 => _
b: the shift (intercept analog) parameter: b = 0 => __/ , b = 2 => __/ 0 0
x: the scalar to be rectified

Attributes

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

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

runMain scalation.modeling.sumQueueTest

Attributes

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

runMain scalation.modeling.sumQueueTest2

Attributes

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 "LSET (...)" and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symLassoRegressionTest

Attributes

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

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

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

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

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

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 "LSET (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

runMain scalation.modeling.symLassoRegressionTest7

Attributes

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

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

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 "LSET (...)" and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symRidgeRegressionTest

Attributes

The symRidgeRegressionTest14 main function tests the SymRidgeRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Regression", with powers specified in "LSET (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

runMain scalation.modeling.symRidgeRegressionTest14

Attributes

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

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

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

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

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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

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 "LSET (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

runMain scalation.modeling.symRidgeRegressionTest7

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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

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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

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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 "LSET (...)" and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symbolicRegressionTest

Attributes

The symbolicRegressionTest10 main function tests the SymbolicRegression object using the Forest Fires dataset. Assumes no missing values. It tests "Quadratic Regression" (with cross = false/true) and applies forward selection, backward elimination, or stepwise regression.

runMain scalation.modeling.symbolicRegressionTest10

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The symbolicRegressionTest11 main function tests the SymbolicRegression object using the Forest Fires dataset. Assumes no missing values. It tests "Cubic Regression" (with cross = false, the default) and applies forward selection, backward elimination, or stepwise regression. It illustrates the conversion of string columns into ORDINAL/integer columns.

runMain scalation.modeling.symbolicRegressionTest11

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The symbolicRegressionTest12 main function tests the SymbolicRegression object using the Forest Fires dataset. Assumes no missing values. It tests "Cubic Regression" (with cross = false, the default) and applies forward selection, backward elimination, or stepwise regression. It illustrates the conversion of string columns into ORDINAL/integer columns. Then the day ordinal column (3) is converted to six DUMMY VARIABLE columns that are NOT expanded.

runMain scalation.modeling.symbolicRegressionTest12

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The symbolicRegressionTest13 main function tests the SymbolicRegression object using a simple dataset to compare Regression and Quadratic Regression.

runMain scalation.modeling.symbolicRegressionTest13

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The symbolicRegressionTest14 main function tests the SymbolicRegression object using the AutoMPG dataset. Assumes no missing values. It tests custom "Symbolic Regression", with powers specified in "LSET (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

runMain scalation.modeling.symbolicRegressionTest14

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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

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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

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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

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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

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 explosion of terms.

runMain scalation.modeling.symbolicRegressionTest6

Attributes

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 "LSET (...)" and applies forward selection, backward elimination, or stepwise regression. This test case performs data rescaling.

runMain scalation.modeling.symbolicRegressionTest7

Attributes

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

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

runMain scalation.modeling.symbolicRegressionTest9

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The tranRegression2Test main function tests TranRegression2 class using the following regression equation. log (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

runMain scalation.modeling.tranRegression2Test

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The tranRegression2Test2 main function tests TranRegression2 class using the following regression equation. sqrt (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

runMain scalation.modeling.tranRegression2Test2

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The tranRegression2Test3 main function tests TranRegression2 class using the following regression equation and uses the simulated data in TranRegression2Ex. sqrt (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

Attributes

See also: 5.13.9 exercises 1, 2, and 3.

runMain scalation.modeling.tranRegression2Test3

The tranRegression2Test4 main function tests TranRegression2 class using the following regression equation. sqrt (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

runMain scalation.modeling.tranRegression2Test4

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The tranRegression2Test5 main function tests TranRegression2 class using the following regression equation. sigmoid^{-1} (y) = b dot x = b_0 + b_1x_1 + b_2x_2.

runMain scalation.modeling.tranRegression2Test5

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The tranRegression2Test6 main function tests TranRegression2 class using the following regression equation on the beer foam dataset.

Attributes

See also: 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.tranRegression2Test6

The tranRegression2Test7 main function tests the TranRegression2 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.tranRegression2Test7

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The tranRegression2Test8 main function tests and compares Regression vs. SymbolicRegression.quadratic vs. TranRegression2. 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.tranRegression2Test8

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The tranRegression2Test9 main function tests the Box-Cox and Yeo-Johnson Transformations.

runMain scalation.modeling.tranRegression2Test9

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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

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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

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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: 5.13.9 exercises 1, 2, and 3.

runMain scalation.modeling.tranRegressionTest3

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

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The tranRegressionTest5 main function tests the TranRegression 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.tranRegressionTest5

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

Attributes

See also: 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

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

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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

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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

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

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

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

Update the key metrics, e.g., rSq-based and smape QoF results for the next iteration of feature selection.

Value parameters

best: the best step so far
cross: indicator to include "many" cross-validation, "one" validation, or "none" nothing
rSq: the VEC containing information about r-Sq-based QoF measures

Attributes

See also: Predictor

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en.wikipedia.org/wiki/Activation_function Convention: fun activation function (e.g., sigmoid) fun_ vector version of activation function (e.g., sigmoid_) funD vector version of dervivative (e.g., sigmoidD)

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