Implementation of the Quadratic loss function. More...

#include <quadratic.h>

Inheritance diagram for slope::Quadratic:

Collaboration diagram for slope::Quadratic:

Public Member Functions
double	loss (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Calculates the quadratic (least-squares) loss.

double	dual (const Eigen::MatrixXd &theta, const Eigen::MatrixXd &y, const Eigen::VectorXd &w)
	Computes the dual function for the quadratic loss.

Eigen::MatrixXd	residual (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Calculates residuals for the quadratic model.

Eigen::MatrixXd	preprocessResponse (const Eigen::MatrixXd &y)
	Preprocesses the response for the quadratic model.

void	updateWeightsAndWorkingResponse (Eigen::VectorXd &w, Eigen::VectorXd &z, const Eigen::VectorXd &eta, const Eigen::VectorXd &y)
	Updates weights and working response for IRLS algorithm.

Eigen::MatrixXd	link (const Eigen::MatrixXd &mu)
	The link function.

Eigen::MatrixXd	inverseLink (const Eigen::MatrixXd &eta)
	The link function, also known as the mean function.

Eigen::MatrixXd	predict (const Eigen::MatrixXd &eta)
	Return predicted response, which is the same as the linear predictor.

Public Member Functions inherited from slope::Loss
virtual	~Loss ()=default
	Destructor for the Loss class.

virtual void	updateIntercept (Eigen::VectorXd &beta0, const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Updates the intercept with a gradient descent update. Also updates the linear predictor (but not the residual).

virtual double	deviance (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Computes deviance, which is 2 times the difference between the loglikelihood of the model and the loglikelihood of the null (intercept-only) model.

Additional Inherited Members
Protected Member Functions inherited from slope::Loss
	Loss (double lipschitz_constant)
	Constructs an loss function with specified Lipschitz constant.

Detailed Description

Implementation of the Quadratic loss function.

The Quadratic class provides methods for computing loss, dual function, residuals, and weight updates for the Quadratic case in the SLOPE algorithm. It is particularly suited for regression problems where the error terms are assumed to follow a normal distribution.

Note: This class inherits from the base Loss class and implements all required virtual functions.

Definition at line 27 of file quadratic.h.

Constructor & Destructor Documentation

◆ Quadratic()

slope::Quadratic::Quadratic ( )

inlineexplicit

Definition at line 30 of file quadratic.h.

Member Function Documentation

◆ dual()

double slope::Quadratic::dual	(	const Eigen::MatrixXd &	theta,
		const Eigen::MatrixXd &	y,
		const Eigen::VectorXd &	w
	)

virtual

Computes the dual function for the quadratic loss.

Calculates the Fenchel conjugate of the quadratic loss function

Parameters

theta	Dual variables vector (n x 1)
y	Observed values vector (n x 1)
w	Observation weights vector (n x 1)

Returns: Double precision dual value

See also: loss() for the primal function

Implements slope::Loss.

Definition at line 12 of file quadratic.cpp.

◆ inverseLink()

Eigen::MatrixXd slope::Quadratic::inverseLink ( const Eigen::MatrixXd & eta )

virtual

The link function, also known as the mean function.

Parameters

eta	Linear predictor.

Returns: The identity function.

Implements slope::Loss.

Definition at line 50 of file quadratic.cpp.

◆ link()

Eigen::MatrixXd slope::Quadratic::link ( const Eigen::MatrixXd & mu )

virtual

The link function.

Parameters

mu Mean.

Returns: The identity function.

Implements slope::Loss.

Definition at line 44 of file quadratic.cpp.

◆ loss()

double slope::Quadratic::loss	(	const Eigen::MatrixXd &	eta,
		const Eigen::MatrixXd &	y
	)

virtual

Calculates the quadratic (least-squares) loss.

Computes the squared error loss between predicted and actual values, normalized by twice the number of observations.

Parameters

eta	Vector of predicted values (n x 1)
y	Matrix of actual values (n x 1)

Returns: Double precision loss value

Note: The loss is calculated as: \( \frac{1}{2n} \sum_{i=1}^n (\eta_i - y_i)^2 \)

Implements slope::Loss.

Definition at line 6 of file quadratic.cpp.

◆ predict()

Eigen::MatrixXd slope::Quadratic::predict ( const Eigen::MatrixXd & eta )

virtual

Return predicted response, which is the same as the linear predictor.

Parameters

eta	The linear predictor

Returns: The predicted response.

Implements slope::Loss.

Definition at line 56 of file quadratic.cpp.

◆ preprocessResponse()

Eigen::MatrixXd slope::Quadratic::preprocessResponse ( const Eigen::MatrixXd & y )

virtual

Preprocesses the response for the quadratic model.

Doesn't perform any transformation on the response.

Parameters

y	Responnse vector (n x 1)

Returns: Modified response

Implements slope::Loss.

Definition at line 28 of file quadratic.cpp.

◆ residual()

Eigen::MatrixXd slope::Quadratic::residual	(	const Eigen::MatrixXd &	eta,
		const Eigen::MatrixXd &	y
	)

virtual

Calculates residuals for the quadratic model.

Computes the difference between observed and predicted values

Parameters

eta	Predicted values vector (n x 1)
y	Actual values vector (n x 1)

Returns: Vector of residuals (n x 1)

Note: Residuals are calculated as: \( r_i = \eta_i - y_i \)

Implements slope::Loss.

Definition at line 22 of file quadratic.cpp.

◆ updateWeightsAndWorkingResponse()

void slope::Quadratic::updateWeightsAndWorkingResponse	(	Eigen::VectorXd &	w,
		Eigen::VectorXd &	z,
		const Eigen::VectorXd &	eta,
		const Eigen::VectorXd &	y
	)

virtual

Updates weights and working response for IRLS algorithm.

For quadratic case, weights are set to 1 and working response equals the original response. This implementation is particularly simple compared to other GLM families.

Parameters

[out]	w	Weights vector to be updated (n x 1)
[out]	z	Working response vector to be updated (n x 1)
[in]	eta	Current predictions vector (n x 1)
[in]	y	Matrix of observed values (n x 1)

Note: For quadratic regression, this is particularly simple as weights remain constant and working response equals the original response

Implements slope::Loss.

Definition at line 34 of file quadratic.cpp.

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

src/slope/losses/quadratic.h
src/slope/losses/quadratic.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Quadratic()

Member Function Documentation

◆ dual()

◆ inverseLink()

◆ link()

◆ loss()

◆ predict()

◆ preprocessResponse()

◆ residual()

◆ updateWeightsAndWorkingResponse()