Table of Contents

Class RidgeRegression<T>

Namespace
AiDotNet.Regression
Assembly
AiDotNet.dll

Implements Ridge Regression (L2 regularized linear regression), which extends ordinary least squares by adding a penalty term proportional to the squared magnitude of the coefficients.

public class RidgeRegression<T> : RegressionBase<T>, IRegression<T>, IFullModel<T, Matrix<T>, Vector<T>>, IModel<Matrix<T>, Vector<T>, ModelMetadata<T>>, IModelSerializer, ICheckpointableModel, IParameterizable<T, Matrix<T>, Vector<T>>, IFeatureAware, IFeatureImportance<T>, ICloneable<IFullModel<T, Matrix<T>, Vector<T>>>, IGradientComputable<T, Matrix<T>, Vector<T>>, IJitCompilable<T>

Type Parameters

T

The numeric type used for calculations (typically float or double).

Inheritance
RidgeRegression<T>
Implements
IFullModel<T, Matrix<T>, Vector<T>>
IModel<Matrix<T>, Vector<T>, ModelMetadata<T>>
IParameterizable<T, Matrix<T>, Vector<T>>
ICloneable<IFullModel<T, Matrix<T>, Vector<T>>>
IGradientComputable<T, Matrix<T>, Vector<T>>
Inherited Members
Extension Methods

Remarks

Ridge Regression solves the following optimization problem: minimize ||y - Xw||^2 + alpha * ||w||^2

This has a closed-form solution: w = (X^T X + alpha * I)^(-1) X^T y

The L2 penalty shrinks coefficients toward zero but never sets them exactly to zero, making Ridge Regression suitable for problems where all features are expected to contribute.

For Beginners: Ridge Regression is a safer version of linear regression.

Regular linear regression can become unstable when:

  • You have many features relative to samples
  • Some features are highly correlated with each other
  • The data contains noise

Ridge Regression fixes these issues by adding a "penalty" for large coefficients:

  • It prevents any single feature from dominating the prediction
  • It makes the model more stable and reliable
  • It typically improves predictions on new, unseen data

Think of it like putting rubber bands on a flexible ruler - the bands (regularization) keep the ruler from bending too wildly (overfitting), while still allowing it to follow the general trend of the data.

Example usage:

var options = new RidgeRegressionOptions<double> { Alpha = 1.0 };
var ridge = new RidgeRegression<double>(options);
ridge.Train(features, targets);
var predictions = ridge.Predict(newFeatures);

Constructors

RidgeRegression(RidgeRegressionOptions<T>?, IRegularization<T, Matrix<T>, Vector<T>>?)

Initializes a new instance of the RidgeRegression<T> class.

public RidgeRegression(RidgeRegressionOptions<T>? options = null, IRegularization<T, Matrix<T>, Vector<T>>? regularization = null)

Parameters

options RidgeRegressionOptions<T>

Configuration options for Ridge Regression. If null, default options are used.

regularization IRegularization<T, Matrix<T>, Vector<T>>

Optional additional regularization strategy.

Remarks

Creates a new Ridge Regression model with the specified options. The primary regularization is controlled by the Alpha parameter in the options. An additional regularization strategy can be provided for more complex regularization schemes.

For Beginners: This creates a new Ridge Regression model.

You can customize the model by providing options:

// Create with default options (alpha = 1.0)
var ridge = new RidgeRegression<double>();

// Create with custom alpha
var options = new RidgeRegressionOptions<double> { Alpha = 0.5 };
var ridge = new RidgeRegression<double>(options);

Methods

CreateNewInstance()

Creates a new instance of Ridge Regression with the same configuration.

protected override IFullModel<T, Matrix<T>, Vector<T>> CreateNewInstance()

Returns

IFullModel<T, Matrix<T>, Vector<T>>

A new instance with the same options.

Deserialize(byte[])

Deserializes a Ridge Regression model from a byte array.

public override void Deserialize(byte[] modelData)

Parameters

modelData byte[]

The byte array containing the serialized model.

GetModelMetadata()

Gets metadata about the Ridge Regression model.

public override ModelMetadata<T> GetModelMetadata()

Returns

ModelMetadata<T>

A ModelMetadata object containing model information.

GetModelType()

Gets the model type identifier.

protected override ModelType GetModelType()

Returns

ModelType

The ModelType enumeration value for Ridge Regression.

Serialize()

Serializes the Ridge Regression model to a byte array.

public override byte[] Serialize()

Returns

byte[]

A byte array containing the serialized model.

Train(Matrix<T>, Vector<T>)

Trains the Ridge Regression model using the provided training data.

public override void Train(Matrix<T> x, Vector<T> y)

Parameters

x Matrix<T>

The input features matrix where each row is a sample and each column is a feature.

y Vector<T>

The target values vector corresponding to each sample.

Remarks

Training computes the closed-form solution: w = (X^T X + alpha * I)^(-1) X^T y

This is numerically stable due to the regularization term, which ensures the matrix X^T X + alpha * I is always invertible (positive definite).

For Beginners: This method teaches the model to make predictions from your data.

The training process:

  1. Adds an intercept column (if UseIntercept = true)
  2. Computes the optimal coefficients using a direct mathematical formula
  3. Stores the coefficients for making predictions later

Unlike some other methods, Ridge Regression has a direct solution - no iterative optimization is needed, making training fast and deterministic.

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