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

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	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...

bool	Intercept () const
	Return whether or not an intercept term is used in the model. More...

double	Lambda () const
	Return the Tikhonov regularization parameter for ridge regression. More...

double &	Lambda ()
	Modify the Tikhonov regularization parameter for ridge regression. More...

const arma::vec &	Parameters () const
	Return the parameters (the b vector). More...

arma::vec &	Parameters ()
	Modify the parameters (the b vector). More...

void	Predict (const arma::mat &points, arma::rowvec &predictions) const
	Calculate y_i for each data point in points. More...

template < typename Archive >
void	serialize (Archive &ar, const uint32_t)
	Serialize the model. 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...

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.

Definition at line 26 of file linear_regression.hpp.

Constructor & Destructor Documentation

◆ LinearRegression() [1/3]

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	(	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]

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()!

Definition at line 62 of file linear_regression.hpp.

References LinearRegression::ComputeError(), LinearRegression::Predict(), and LinearRegression::Train().

Member Function Documentation

◆ ComputeError()

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.

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).

Referenced by LinearRegression::LinearRegression(), and RegressionDistribution::RegressionDistribution().

◆ Intercept()

bool Intercept ( ) const

inline

Return whether or not an intercept term is used in the model.

Definition at line 137 of file linear_regression.hpp.

◆ Lambda() [1/2]

double Lambda ( ) const

inline

Return the Tikhonov regularization parameter for ridge regression.

Definition at line 132 of file linear_regression.hpp.

◆ Lambda() [2/2]

double& Lambda ( )

inline

Modify the Tikhonov regularization parameter for ridge regression.

Definition at line 134 of file linear_regression.hpp.

◆ Parameters() [1/2]

const arma::vec& Parameters ( ) const

inline

Return the parameters (the b vector).

Definition at line 127 of file linear_regression.hpp.

Referenced by RegressionDistribution::Dimensionality(), and RegressionDistribution::Parameters().

◆ Parameters() [2/2]

arma::vec& Parameters ( )

inline

Modify the parameters (the b vector).

Definition at line 129 of file linear_regression.hpp.

◆ Predict()

void 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.

Referenced by LinearRegression::LinearRegression().

◆ serialize()

void serialize	(	Archive &	ar,
		const uint32_t
	)

inline

Serialize the model.

Definition at line 143 of file linear_regression.hpp.

◆ Train() [1/2]

double 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.

Referenced by LinearRegression::LinearRegression(), and RegressionDistribution::RegressionDistribution().

◆ Train() [2/2]

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.

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.

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

/home/ryan/src/mlpack.org/_src/mlpack-git/src/mlpack/methods/linear_regression/linear_regression.hpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ LinearRegression() [1/3]

◆ LinearRegression() [2/3]

◆ LinearRegression() [3/3]

Member Function Documentation

◆ ComputeError()

◆ Intercept()

◆ Lambda() [1/2]

◆ Lambda() [2/2]

◆ Parameters() [1/2]

◆ Parameters() [2/2]

◆ Predict()

◆ serialize()

◆ Train() [1/2]

◆ Train() [2/2]