Table of Contents

Class MultivariateRegression<T>

Namespace
AiDotNet.Regression
Assembly
AiDotNet.dll

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

public class MultivariateRegression<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
MultivariateRegression<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

Multivariate linear regression is a statistical method that models the relationship between multiple independent variables and a 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) if included.

For Beginners: Multivariate regression is like a recipe that combines several ingredients to predict an outcome.

Think of it like a car's fuel efficiency calculator:

  • You provide information like car weight, engine size, aerodynamics, etc.
  • Each factor has a certain importance (coefficient) in determining fuel efficiency
  • The model combines all these factors to make a prediction

For example, the formula might be: Miles per gallon = 35 - (0.005 × Car Weight) - (2 × Engine Size) + (3 × Aerodynamic Rating)

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

Constructors

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

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

public MultivariateRegression(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 multivariate 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 multivariate 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 fitting too closely to the training data

Regularization is like adding a rule that says "keep things simple unless there's strong evidence." This typically helps the model perform better on new data it hasn't seen before.

Methods

CreateNewInstance()

Creates a new instance of the Multivariate 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 Multivariate Regression model.

Remarks

This method creates a deep copy of the current Multivariate Regression model, including its coefficients, intercept, and configuration options. 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 your trained model.

Think of it like making a perfect duplicate of your recipe:

  • It copies all the configuration settings (like whether to use an intercept)
  • It preserves the coefficients (the importance values for each feature)
  • It maintains the intercept (the starting point or base value)

Creating a copy is useful when you want to:

  • Create a backup before further modifying the model
  • Create variations of the same model for different purposes
  • Share the model with others 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, MultivariateRegression.

Remarks

This method returns an enumeration value indicating that this is a multivariate 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 (MultivariateRegression) that:

  • Identifies this specific type of model
  • Helps other code handle the model appropriately
  • Is used when saving or loading models

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

Predict(Matrix<T>)

Makes predictions for new data points using the trained multivariate regression model.

public override Vector<T> Predict(Matrix<T> input)

Parameters

input Matrix<T>

The feature matrix where each row is a sample to predict.

Returns

Vector<T>

A vector containing the predicted values.

Remarks

This method makes predictions by applying the learned coefficients to the input features. If an intercept term is used, it is added to the feature matrix before multiplication. The prediction is calculated as: y = X * coefficients (+ intercept if enabled).

For Beginners: This is where the model uses what it learned to make predictions on new data.

The prediction process:

  1. For each data point, take its feature values
  2. Multiply each feature by its corresponding coefficient
  3. Add all these products together (plus the intercept if used)
  4. The result is the predicted value

It's like following a recipe with precise measurements:

  • 0.005 units of effect for each unit of the first feature
  • 2 units of effect for each unit of the second feature
  • And so on for each feature

The model combines all these effects to produce the final prediction.

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

Trains the multivariate 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 multivariate 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 mathematical 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, multivariate regression finds the optimal solution in one step by solving a mathematical equation.

For example, the model might learn that for car fuel efficiency:

  • Each additional pound of weight reduces efficiency by 0.005 mpg
  • Each liter of engine size reduces efficiency by 2 mpg
  • Each point in aerodynamic rating improves efficiency by 3 mpg
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