Table of Contents

Interface ILinearRegression<T>

Namespace
AiDotNet.Interfaces
Assembly
AiDotNet.dll

Defines an interface for linear regression in machine learning, which predict outputs as a weighted sum of inputs plus an optional constant.

public interface ILinearRegression<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., double, float).

Inherited Members
Extension Methods

Remarks

For Beginners: This interface represents the simplest and most fundamental type of machine learning model.

Imagine you're trying to predict house prices based on features like:

  • Square footage
  • Number of bedrooms
  • Age of the house

A linear model works like this:

  • Each feature gets assigned a "weight" (coefficient) that represents its importance
  • For example: Each square foot might add $100 to the price
  • Each bedroom might add $15,000 to the price
  • Each year of age might subtract $500 from the price
  • There might also be a "starting price" (intercept) of $50,000

To make a prediction, the model:

  1. Multiplies each feature by its weight
  2. Adds all these values together
  3. Adds the intercept (if there is one)

So for a 2,000 sq ft, 3-bedroom, 10-year-old house: Price = $50,000 + (2,000 × $100) + (3 × $15,000) + (10 × -$500) Price = $50,000 + $200,000 + $45,000 - $5,000 Price = $290,000

Linear models are popular because they're:

  • Simple to understand
  • Fast to train
  • Easy to interpret (you can see exactly how each feature affects the prediction)
  • Often surprisingly effective despite their simplicity

Properties

Coefficients

Gets the weights (coefficients) assigned to each input feature in the linear model.

Vector<T> Coefficients { get; }

Property Value

Vector<T>

Remarks

For Beginners: These are the numbers that determine how important each input feature is to your prediction.

In our house price example:

  • The coefficient for square footage might be 100 (each square foot adds $100)
  • The coefficient for bedrooms might be 15000 (each bedroom adds $15,000)
  • The coefficient for house age might be -500 (each year subtracts $500)

Positive coefficients mean that as the feature increases, the prediction increases. Negative coefficients mean that as the feature increases, the prediction decreases.

The size of the coefficient (whether it's a large or small number) tells you how strongly that feature influences the prediction.

This property returns all coefficients as a vector (essentially a list of numbers), where each position corresponds to a specific input feature.

HasIntercept

Gets a value indicating whether this linear model includes an intercept term.

bool HasIntercept { get; }

Property Value

bool

Remarks

For Beginners: This tells you whether the model includes a "starting value" (intercept) or not.

When this is true:

  • The model includes an intercept term (the base value)
  • Predictions are calculated as: Intercept + (Feature1 × Weight1) + (Feature2 × Weight2) + ...

When this is false:

  • The model does not include an intercept term
  • Predictions are calculated as: (Feature1 × Weight1) + (Feature2 × Weight2) + ...
  • When all features are zero, the prediction will be exactly zero

Most linear models include an intercept (HasIntercept = true) because it gives the model more flexibility to fit the data. However, in some special cases, you might want to force the model to pass through the origin (0,0), which requires HasIntercept = false.

Intercept

Gets the constant term (bias) added to the weighted sum of features in the linear model.

T Intercept { get; }

Property Value

T

Remarks

For Beginners: This is the "starting value" or "base value" for your prediction before considering any of the input features.

In our house price example:

  • The intercept might be $50,000, meaning that's the base price before we consider square footage, bedrooms, or age

The intercept allows the model to make reasonable predictions even when some feature values are zero. For example, a house with zero square footage doesn't make sense, but the model still needs to produce reasonable values.

Some models don't use an intercept (when HasIntercept is false), which forces the prediction to be zero when all features are zero.

Edit this page