mlpack::regression::LinearRegression Class Reference

A simple linear regression algorithm using ordinary least squares. More...

#include <linear_regression.hpp>

Public Member Functions
	LinearRegression (const arma::mat &predictors, const arma::rowvec &responses, const double lambda=0, const bool intercept=true)
	Creates the model. More...
	LinearRegression (const arma::mat &predictors, const arma::rowvec &responses, const arma::rowvec &weights, const double lambda=0, const bool intercept=true)
	Creates the model with weighted learning. More...
	LinearRegression ()
	Empty constructor. More...
double	Train (const arma::mat &predictors, const arma::rowvec &responses, const bool intercept=true)
	Train the LinearRegression model on the given data. More...
double	Train (const arma::mat &predictors, const arma::rowvec &responses, const arma::rowvec &weights, const bool intercept=true)
	Train the LinearRegression model on the given data and weights. More...
void	Predict (const arma::mat &points, arma::rowvec &predictions) const
	Calculate y_i for each data point in points. More...
double	ComputeError (const arma::mat &points, const arma::rowvec &responses) const
	Calculate the L2 squared error on the given predictors and responses using this linear regression model. More...
const arma::vec &	Parameters () const
	Return the parameters (the b vector).
arma::vec &	Parameters ()
	Modify the parameters (the b vector).
double	Lambda () const
	Return the Tikhonov regularization parameter for ridge regression.
double &	Lambda ()
	Modify the Tikhonov regularization parameter for ridge regression.
bool	Intercept () const
	Return whether or not an intercept term is used in the model.
template<typename Archive >
void	serialize (Archive &ar, const uint32_t)
	Serialize the model.

Detailed Description

A simple linear regression algorithm using ordinary least squares.

Optionally, this class can perform ridge regression, if the lambda parameter is set to a number greater than zero.

Constructor & Destructor Documentation

LinearRegression() [1/3]

LinearRegression::LinearRegression	(	const arma::mat &	predictors,
		const arma::rowvec &	responses,
		const double	lambda = 0,
		const bool	intercept = true
	)

Creates the model.

Parameters

predictors	X, matrix of data points.
responses	y, the measured data for each point in X.
lambda	Regularization constant for ridge regression.
intercept	Whether or not to include an intercept term.

LinearRegression() [2/3]

LinearRegression::LinearRegression	(	const arma::mat &	predictors,
		const arma::rowvec &	responses,
		const arma::rowvec &	weights,
		const double	lambda = 0,
		const bool	intercept = true
	)

Creates the model with weighted learning.

Parameters

predictors	X, matrix of data points.
responses	y, the measured data for each point in X.
weights	Observation weights (for boosting).
lambda	Regularization constant for ridge regression.
intercept	Whether or not to include an intercept term.

LinearRegression() [3/3]

mlpack::regression::LinearRegression::LinearRegression ( )

inline

Empty constructor.

This gives a non-working model, so make sure Train() is called (or make sure the model parameters are set) before calling Predict()!

Member Function Documentation

ComputeError()

double LinearRegression::ComputeError	(	const arma::mat &	points,
		const arma::rowvec &	responses
	)		const

Calculate the L2 squared error on the given predictors and responses using this linear regression model.

This calculation returns

\[ (1 / n) * \| y - X B \|^2_2 \]

where \( y \) is the responses vector, \( X \) is the matrix of predictors, and \( B \) is the parameters of the trained linear regression model.

As this number decreases to 0, the linear regression fit is better.

Parameters

points	Matrix of predictors (X).
responses	Transposed vector of responses (y^T).

Predict()

void LinearRegression::Predict	(	const arma::mat &	points,
		arma::rowvec &	predictions
	)		const

Calculate y_i for each data point in points.

Parameters

points	the data points to calculate with.
predictions	y, will contain calculated values on completion.

Train() [1/2]

double LinearRegression::Train	(	const arma::mat &	predictors,
		const arma::rowvec &	responses,
		const bool	intercept = true
	)

Train the LinearRegression model on the given data.

Careful! This will completely ignore and overwrite the existing model. This particular implementation does not have an incremental training algorithm. To set the regularization parameter lambda, call Lambda() or set a different value in the constructor.

Parameters

predictors	X, the matrix of data points to train the model on.
responses	y, the responses to the data points.
intercept	Whether or not to fit an intercept term.

Returns

The least squares error after training.

Train() [2/2]

double LinearRegression::Train	(	const arma::mat &	predictors,
		const arma::rowvec &	responses,
		const arma::rowvec &	weights,
		const bool	intercept = true
	)

Train the LinearRegression model on the given data and weights.

Careful! This will completely ignore and overwrite the existing model. This particular implementation does not have an incremental training algorithm. To set the regularization parameter lambda, call Lambda() or set a different value in the constructor.

Parameters

predictors	X, the matrix of data points to train the model on.
responses	y, the responses to the data points.
weights	Observation weights (for boosting).
intercept	Whether or not to fit an intercept term.

Returns

The least squares error after training.

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The documentation for this class was generated from the following files:

• src/mlpack/methods/linear_regression/linear_regression.hpp
• src/mlpack/methods/linear_regression/linear_regression.cpp