Table of Contents

Class RegressionOptions<T>

Namespace
AiDotNet.Models.Options
Assembly
AiDotNet.dll

Configuration options for regression models, which are statistical methods used to estimate relationships between variables and make predictions.

public class RegressionOptions<T> : ModelOptions

Type Parameters

T

The data type used in matrix operations for the regression model.

Inheritance
RegressionOptions<T>
Derived
Inherited Members

Remarks

Regression analysis is a fundamental statistical technique used to model the relationship between a dependent variable and one or more independent variables. This class provides configuration options for regression models, allowing customization of how the regression algorithm operates. Regression models are widely used in machine learning and statistics for prediction, forecasting, and understanding variable relationships. Common regression types include linear regression, polynomial regression, and regularized regression methods like ridge and lasso regression.

For Beginners: Regression is a way to find patterns in your data that help predict numbers.

Think about predicting house prices:

  • You have information like square footage, number of bedrooms, and neighborhood
  • Regression helps you create a formula that uses these features to predict the price
  • The formula might look like: Price = (Square Footage × Factor1) + (Bedrooms × Factor2) + BaseValue

What regression does:

  • It analyzes your existing data (houses with known prices)
  • It finds the best values for each factor in the formula
  • It creates a model that can predict prices for new houses

This is useful when:

  • You need to predict a numerical value (like price, temperature, or sales)
  • You have data with features that might influence that value
  • You want to understand how much each feature contributes to the prediction

For example, a weather app might use regression to predict tomorrow's temperature based on today's readings, humidity levels, and seasonal patterns.

This class lets you configure how the regression model is constructed and calculated.

Properties

DecompositionMethod

Gets or sets the matrix decomposition method used in the regression calculations.

public IMatrixDecomposition<T>? DecompositionMethod { get; set; }

Property Value

IMatrixDecomposition<T>

An implementation of IMatrixDecomposition<T> or null to use the default method.

Remarks

Matrix decomposition is a crucial mathematical technique used in solving regression problems, especially when dealing with systems of linear equations. Different decomposition methods have varying characteristics in terms of numerical stability, computational efficiency, and applicability to specific problem types. Common decomposition methods include Singular Value Decomposition (SVD), QR decomposition, Cholesky decomposition, and LU decomposition. The choice of decomposition method can significantly impact the accuracy and performance of the regression algorithm, particularly for ill-conditioned problems or large datasets.

For Beginners: Matrix decomposition is a mathematical technique that helps solve complex equations more efficiently.

Think of it like breaking down a difficult math problem into simpler steps:

  • Regression often involves solving systems of equations with many variables
  • These equations can be represented as matrices (tables of numbers)
  • Matrix decomposition breaks these complex matrices into simpler components
  • This makes calculations faster, more accurate, and more stable

Different decomposition methods have different strengths:

  • Some are faster but less accurate for certain problems
  • Some handle special cases better (like when variables are highly correlated)
  • Some are more numerically stable (less likely to have rounding errors)

You can leave this setting as null (the default) to let the algorithm choose an appropriate method, or specify a particular decomposition method if you have specific requirements or knowledge about your data's characteristics.

Unless you have a specific reason to change this, it's usually best to leave it as the default.

UseIntercept

Gets or sets whether the regression model should include an intercept term (also known as bias term).

public bool UseIntercept { get; set; }

Property Value

bool

True to include an intercept term; false to force the regression line through the origin. Default is true.

Remarks

The intercept term (also called the bias or constant term) represents the expected value of the dependent variable when all independent variables are zero. Including an intercept allows the regression line to "float" and not be constrained to pass through the origin. This is appropriate for most real-world problems where a baseline value exists even when predictor variables are zero. In some specific scientific or engineering contexts where a zero input must theoretically produce a zero output, setting UseIntercept to false may be more appropriate. The decision to include or exclude an intercept should be based on domain knowledge and the specific requirements of the modeling task.

For Beginners: This setting determines whether your prediction formula includes a "starting value" or base amount.

Using our house price example:

  • With UseIntercept = true (default): Price = (Square Footage × Factor1) + (Bedrooms × Factor2) + BaseValue
  • With UseIntercept = false: Price = (Square Footage × Factor1) + (Bedrooms × Factor2)

The difference is that "BaseValue" (the intercept):

  • Represents the predicted price when all other factors are zero
  • Allows the model to have a starting point that isn't zero
  • Makes the model more flexible for most real-world problems

When to use true (include intercept):

  • Most real-world scenarios (the default and recommended for beginners)
  • When you expect there to be some base value even when all features are zero
  • For example, even a 0 square foot house with 0 bedrooms might still have some land value

When to use false (no intercept):

  • When you know theoretically that zero input should produce zero output
  • In scientific models where this constraint is physically meaningful
  • For example, if measuring how far a spring stretches based on weight, zero weight means zero stretch

For most applications, keep this set to true unless you have a specific reason to change it.

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