Table of Contents

Class PolynomialRegression<T>

Namespace
AiDotNet.Regression
Assembly
AiDotNet.dll

Implements polynomial regression, which extends linear regression by fitting a polynomial equation to the data.

public class PolynomialRegression<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 (e.g., float, double).

Inheritance
PolynomialRegression<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

Polynomial regression is useful when the relationship between variables is not linear. It works by creating new features that are powers of the original features (x, x², x³, etc.), then applying linear regression techniques to these expanded features.

For Beginners: While linear regression fits a straight line to your data, polynomial regression can fit curves, allowing it to capture more complex patterns.

Constructors

PolynomialRegression(PolynomialRegressionOptions<T>?, IRegularization<T, Matrix<T>, Vector<T>>?)

Creates a new instance of the polynomial regression model.

public PolynomialRegression(PolynomialRegressionOptions<T>? options = null, IRegularization<T, Matrix<T>, Vector<T>>? regularization = null)

Parameters

options PolynomialRegressionOptions<T>

Configuration options for the polynomial regression model, including the degree of the polynomial. The degree determines how complex the curve can be (e.g., degree 2 allows for parabolas).

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

Optional regularization method to prevent overfitting. Regularization adds a penalty for large coefficient values, which helps create a more generalizable model.

Remarks

For Beginners: The degree of the polynomial determines how "curvy" your model can be. A higher degree (like 3 or 4) allows for more complex curves but may lead to overfitting if you don't have enough data.

Methods

CreateNewInstance()

Creates a new instance of the Polynomial 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 Polynomial Regression model.

Remarks

This method creates a deep copy of the current Polynomial 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 recipe:

  • It copies all the configuration settings (like the polynomial degree)
  • It preserves the coefficients (the weights for each polynomial term)
  • It maintains the intercept (the starting point of your curve)

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 identifier for polynomial regression.

Predict(Matrix<T>)

Makes predictions using the trained polynomial regression model.

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

Parameters

input Matrix<T>

The input feature matrix where each row represents a data point to predict and each column represents a feature.

Returns

Vector<T>

A vector of predicted values, one for each row in the input matrix.

Remarks

For Beginners: Once the model is trained, this method uses the discovered polynomial equation to predict outcomes for new data points. It first transforms the input features into polynomial features, then applies the learned coefficients to make predictions.

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

Trains the polynomial regression model using the provided input features and target values.

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

Parameters

x Matrix<T>

The input feature matrix where each row represents a data point and each column represents a feature.

y Vector<T>

The target values vector where each element corresponds to a row in the input matrix.

Remarks

This method:

  1. Transforms the original features into polynomial features (x, x², x³, etc.)
  2. Adds a constant column for the intercept if specified in the options
  3. Solves the least squares equation to find the optimal coefficients

For Beginners: Training means finding the best curve that fits your data points. The algorithm creates additional features by raising your original features to different powers, then finds the best combination of these features to predict your target values.

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