Represents a regularized (ridge or LASSO) regression model.
SystemObject Extreme.DataAnalysis.ModelsModel Extreme.DataAnalysis.ModelsRegressionModelDouble Extreme.StatisticsRegularizedRegressionModel
Namespace:
Extreme.Statistics
Assembly:
Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
public class RegularizedRegressionModel : RegressionModel<double>
Public Class RegularizedRegressionModel
Inherits RegressionModel(Of Double)
public ref class RegularizedRegressionModel : public RegressionModel<double>
type RegularizedRegressionModel =
class
inherit RegressionModel<float>
endThe RegularizedRegressionModel type exposes the following members.
|
| Name | Description |
|---|
 | RegularizedRegressionModel(IDataFrame, String) | |
| RegularizedRegressionModel(VectorDouble, VectorDouble) |
Constructs a new RegularizedRegressionModel.
|
| RegularizedRegressionModel(IDataFrame, String, String) |
Constructs a new RegularizedRegressionModel.
|
| RegularizedRegressionModel(VectorDouble, MatrixDouble, Boolean, VectorDouble) | |
| RegularizedRegressionModel(IDataFrame, String, String, Boolean, String) | Initializes a new instance of the RegularizedRegressionModel class |
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Use the RegularizedRegressionModel class to analyze
a linear relationship between two or more numerical variables
where the problem is ill-posed.
A multiple linear regression model tries to express one variable,
called the dependent variable, as a linear combination of one or more
other variables called independent variables or predictors.
Regularized regression compensates for the ill-posed nature
of the problem by trading some increase bias for a reduction
in variance.
Two regularization methods are supported by
the RegularizedRegressionModel class: the LASSO
(least absolute shrinkage and selection operator) and elastic net.
Ridge regression can be performed using the
LinearRegressionModel class.
In ordinary least squares, the parameter values are computed
by minimizing the sum of the squared residuals. In the LASSO,
a multiple of the one-norm of the parameters is added to the objective
function. The multiplier is specified as the RegularizationParameter
property.
The elastic net is a generalization of the LASSO that also adds
a multiple of the squared two-norm of the parameters to the objective function.
The ratio of the coefficients is specified through the
RegularizationRatio property. This is a value between 0 and 1.
A value of 1 indicates LASSO (this is the default).
A value of zero indicates ridge regression. However, the calculation of
ridge regression coefficients in this fashion is not reliable.
Reference