slope::Quadratic Class Reference

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	hessianDiagonal (const Eigen::MatrixXd &eta)
	Calculates hessian diagonal.
Eigen::MatrixXd	preprocessResponse (const Eigen::MatrixXd &y)
	Preprocesses the response for the quadratic model.
void	updateWeightsAndWorkingResponse (Eigen::MatrixXd &w, Eigen::MatrixXd &z, const Eigen::MatrixXd &eta, const Eigen::MatrixXd &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.
Eigen::MatrixXd	residual (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Calculates the generalized residual.
virtual void	updateIntercept (Eigen::VectorXd &beta0, const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Updates the intercept with a gradient descent update.
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.

hessianDiagonal()

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

virtual

Calculates hessian diagonal.

Parameters

eta	Linear predictor

Returns

A matrix of ones (n x m)

Implements slope::Loss.

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.

link()

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

virtual

The link function.

Parameters

mu	Mean of the distribution.

Returns

The identity function.

Implements slope::Loss.

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.

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.

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.

updateWeightsAndWorkingResponse()

void slope::Quadratic::updateWeightsAndWorkingResponse ( Eigen::MatrixXd &  w, Eigen::MatrixXd &  z, const Eigen::MatrixXd &  eta, const Eigen::MatrixXd &  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

Reimplemented from slope::Loss.

---

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

• include/slope/losses/quadratic.h