Table of Contents

Class PartialLeastSquaresRegressionOptions<T>

Namespace
AiDotNet.Models.Options
Assembly
AiDotNet.dll

Configuration options for Partial Least Squares Regression (PLS), a technique that combines features of principal component analysis and multiple regression to handle multicollinearity and high-dimensional data.

public class PartialLeastSquaresRegressionOptions<T> : RegressionOptions<T>

Type Parameters

T
Inheritance
PartialLeastSquaresRegressionOptions<T>
Inherited Members

Remarks

Partial Least Squares Regression is a powerful statistical method that finds a linear regression model by projecting both the predictor variables (X) and the response variables (Y) to a new space. Unlike ordinary least squares regression, which can struggle with multicollinearity (highly correlated predictors) and high-dimensional data, PLS creates latent variables (components) that maximize the covariance between X and Y. This approach is particularly valuable in situations where the number of predictor variables exceeds the number of observations, or when predictors are highly correlated. PLS has found wide application in fields such as chemometrics, spectroscopy, and bioinformatics.

For Beginners: Partial Least Squares Regression is a special technique for finding relationships in complex data.

Imagine you're trying to predict house prices based on 50 different measurements:

  • Many of these measurements might be related (like square footage and number of rooms)
  • With so many variables, traditional regression methods might struggle

What PLS does:

  • Instead of using all 50 original measurements directly
  • It creates a smaller set of "super measurements" (called components)
  • Each component combines multiple original measurements in a smart way
  • These components capture the most important patterns relevant to your prediction

Think of it like cooking:

  • Traditional regression uses each ingredient separately
  • PLS creates a few key flavor profiles (combining multiple ingredients)
  • Then uses these flavor profiles to create the final dish

This approach is especially useful when:

  • You have more variables than data points
  • Your variables are highly correlated with each other
  • You need to reduce noise and focus on the most important patterns

This class lets you configure how many of these "super measurements" (components) to use in your analysis.

Properties

NumComponents

Gets or sets the number of latent components to extract in the PLS model.

public int NumComponents { get; set; }

Property Value

int

The number of components, defaulting to 2.

Remarks

This parameter determines how many latent components (also called factors or latent variables) the PLS algorithm will extract. Each component is a linear combination of the original predictor variables, constructed to maximize the covariance with the response variable(s) while maintaining orthogonality with previous components. The optimal number of components depends on the complexity of the relationship between predictors and response, as well as the amount of noise in the data. Too few components may result in underfitting, while too many may lead to overfitting. Cross-validation is often used to determine the optimal number.

For Beginners: This setting controls how many "super measurements" (components) the model will create from your original variables.

The default value of 2 means:

  • The algorithm will create 2 components from your original variables
  • These 2 components will be used to make predictions

Think of it like data compression:

  • Each component captures a certain amount of the important information
  • The first component captures the most important patterns
  • Each additional component captures less and less additional information

You might want more components (like 5 or 10) if:

  • Your data has complex relationships that can't be captured by just a few components
  • You have many original variables with distinct information
  • You have sufficient data to support a more complex model

You might want fewer components (even just 1) if:

  • The relationship is relatively simple
  • You want to prevent overfitting, especially with limited data
  • Your variables are so highly correlated that one component is sufficient

Finding the right number of components is crucial:

  • Too few: The model misses important patterns (underfitting)
  • Too many: The model learns noise in the data (overfitting)

In practice, techniques like cross-validation are often used to find the optimal number of components that gives the best predictive performance.

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