Table of Contents

Class MultipleRegression<T>

Namespace
AiDotNet.Regression
Assembly
AiDotNet.dll

Represents a multiple linear regression model that predicts a target value based on multiple input features.

public class MultipleRegression<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
MultipleRegression<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

Multiple linear regression extends simple linear regression to incorporate multiple input features. It models the relationship between several independent variables and one dependent variable by fitting a linear equation to the observed data. The model assumes that the relationship between inputs and the output is linear, meaning that the output can be calculated as a weighted sum of the input features plus a constant term (intercept).

For Beginners: Multiple regression is like a formula that predicts one value based on several inputs.

Think of it like a house price calculator:

  • You provide information like square footage, number of bedrooms, neighborhood rating, etc.
  • Each feature has a certain importance (called a coefficient)
  • The model combines all these factors with their importances to make a prediction

For example, the formula might be: House Price = $50,000 + ($100 × Square Footage) + ($15,000 × Number of Bedrooms) + ($25,000 × Neighborhood Rating)

The model learns the best values for these coefficients from your training data to make accurate predictions.

Constructors

MultipleRegression(RegressionOptions<T>?, IRegularization<T, Matrix<T>, Vector<T>>?)

Initializes a new instance of the MultipleRegression<T> class with optional custom options and regularization.

public MultipleRegression(RegressionOptions<T>? options = null, IRegularization<T, Matrix<T>, Vector<T>>? regularization = null)

Parameters

options RegressionOptions<T>

Custom options for the regression algorithm. If null, default options are used.

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

Regularization method to prevent overfitting. If null, no regularization is applied.

Remarks

This constructor creates a new multiple regression model with the specified options and regularization. If no options are provided, default values are used. Regularization helps prevent overfitting by penalizing large coefficient values.

For Beginners: This creates a new multiple regression model with your chosen settings.

When creating a regression model:

  • You can provide custom settings (options) or use the defaults
  • You can add regularization, which helps prevent the model from becoming too specialized to the training data

Regularization is like adding a penalty for complexity - it encourages the model to keep the coefficient values smaller, which typically results in a more general model that performs better on new data.

Methods

CreateNewInstance()

Creates a new instance of the Multiple Regression model with the same configuration.

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

Returns

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

A new instance of the Multiple Regression model.

Remarks

This method creates a deep copy of the current Multiple Regression model, including its coefficients, intercept, options, and regularization. The new instance is completely independent of the original, allowing modifications without affecting the original model.

For Beginners: This method creates an exact copy of the current regression model.

The copy includes:

  • The same coefficients (the importance values for each feature)
  • The same intercept (the starting point value)
  • The same options (settings like whether to use an intercept)
  • The same regularization (settings that help prevent overfitting)

This is useful when you want to:

  • Create a backup before modifying the model
  • Create variations of the same model for different purposes
  • Share the model while keeping your original intact

Exceptions

InvalidOperationException

Thrown when the creation fails or required components are null.

GetModelType()

Gets the type of regression model.

protected override ModelType GetModelType()

Returns

ModelType

The model type, in this case, MultipleRegression.

Remarks

This method returns an enumeration value indicating that this is a multiple regression model. This is used for type identification when working with different regression models in a unified manner.

For Beginners: This method simply identifies what kind of model this is.

It returns a label (MultipleRegression) that:

  • Identifies this specific type of model
  • Helps other code handle the model appropriately
  • Is used for model identification and categorization

It's like a name tag that lets other parts of the program know what kind of model they're working with.

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

Trains the multiple regression model using the provided features and target values.

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

Parameters

x Matrix<T>

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

y Vector<T>

The target vector containing the values to predict.

Remarks

This method trains the multiple regression model using the normal equation approach, which finds the optimal coefficients by solving a system of linear equations. The normal equation is given by: coefficients = (X^T * X + regularization)^(-1) * X^T * y, where X^T is the transpose of the feature matrix X. This approach directly computes the optimal coefficients without requiring iterative optimization.

For Beginners: This is where the model learns from your data.

During training:

  1. If an intercept is used, an extra column of 1's is added to the input features
  2. The model applies matrix operations to find the best coefficients
  3. These coefficients determine how much each feature contributes to the prediction

Unlike some other models that learn gradually through many iterations, multiple regression finds the optimal solution in one step by solving a system of equations.

For example, the model might learn that for house prices:

  • Each additional square foot adds $100 to the price
  • Each bedroom adds $15,000 to the price
  • Each point in neighborhood rating adds $25,000 to the price
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