slope::Loss Class Reference

Loss function interface. More...

#include <loss.h>

Inheritance diagram for slope::Loss:

Public Member Functions
virtual	~Loss ()=default
	Destructor for the Loss class.
virtual double	loss (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)=0
	Calculates the loss function.
virtual double	loss (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, const Eigen::VectorXd &observation_weights)
	Calculates the loss averaged by observation weights.
virtual double	dual (const Eigen::MatrixXd &theta, const Eigen::MatrixXd &y, const Eigen::VectorXd &w)=0
	Calculates the dual loss.
Eigen::MatrixXd	residual (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Calculates the generalized residual.
virtual Eigen::MatrixXd	dualPoint (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, bool fit_intercept)
	Constructs a dual candidate from a linear predictor.
virtual Eigen::MatrixXd	dualPoint (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, bool fit_intercept, const Eigen::VectorXd &observation_weights)
	Constructs a dual candidate with weighted intercept stationarity.
virtual Eigen::MatrixXd	hessianDiagonal (const Eigen::MatrixXd &eta)=0
	Calculates the hessian diagonal of the loss function.
virtual void	updateWeightsAndWorkingResponse (Eigen::MatrixXd &w, Eigen::MatrixXd &z, const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Updates weights and working response.
virtual void	updateWeightsAndWorkingResponse (Eigen::MatrixXd &w, Eigen::MatrixXd &z, const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, const Eigen::VectorXd &observation_weights)
	Updates the IRLS approximation including observation weights.
virtual Eigen::MatrixXd	preprocessResponse (const Eigen::MatrixXd &y)=0
	Preprocess response.
virtual void	updateIntercept (Eigen::VectorXd &beta0, const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Updates the intercept with a gradient descent update.
virtual Eigen::MatrixXd	link (const Eigen::MatrixXd &mu)=0
	The link function.
virtual Eigen::MatrixXd	inverseLink (const Eigen::MatrixXd &eta)=0
	The inverse link function, also known as the mean function.
virtual Eigen::MatrixXd	predict (const Eigen::MatrixXd &eta)=0
	Return predicted response.
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.
virtual double	deviance (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, const Eigen::VectorXd &observation_weights)
	Computes deviance averaged by observation weights.

Protected Member Functions
Eigen::MatrixXd	residualOnSupport (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, const Eigen::VectorXd &observation_weights)
	Evaluates family residuals only on positive-weight observations.
	Loss (double lipschitz_constant)
	Constructs an loss function with specified Lipschitz constant.
Eigen::MatrixXd	domainSafePoint (const Eigen::MatrixXd &mean, const Eigen::MatrixXd &y, double lower, double upper) const
	Enforces scalar intercept stationarity without leaving a mean domain.
Eigen::MatrixXd	domainSafePoint (const Eigen::MatrixXd &mean, const Eigen::MatrixXd &y, double lower, double upper, const Eigen::VectorXd &observation_weights) const

Detailed Description

Loss function interface.

This class defines the interface for an loss function, which is used in optimization algorithms. The loss function calculates the loss, dual, residual, and updates the weights and working response.

Definition at line 20 of file loss.h.

Constructor & Destructor Documentation

Loss()

slope::Loss::Loss ( double lipschitz_constant )

inlineexplicitprotected

Constructs an loss function with specified Lipschitz constant.

Parameters

lipschitz_constant

The Lipschitz constant for the loss function

The Lipschitz constant is used to ensure convergence in gradient-based optimization by bounding the rate of change of the gradient.

Definition at line 213 of file loss.h.

Member Function Documentation

deviance()

virtual double slope::Loss::deviance ( const Eigen::MatrixXd & eta, const Eigen::MatrixXd & y )

inlinevirtual

Computes deviance, which is 2 times the difference between the loglikelihood of the model and the loglikelihood of the null (intercept-only) model.

Parameters

eta	The predicted values.
y	The true values.

Definition at line 190 of file loss.h.

domainSafePoint()

Eigen::MatrixXd slope::Loss::domainSafePoint ( const Eigen::MatrixXd & mean, const Eigen::MatrixXd & y, double lower, double upper ) const

protected

Enforces scalar intercept stationarity without leaving a mean domain.

The construction blends the centered residual with the intercept-only feasible point. It is used as a numerical repair after conditional intercept minimization and as a fallback for degenerate responses.

dual()

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

pure virtual

Calculates the dual loss.

This function calculates the dual function given the estimated parameters (theta) and the true values (y).

Parameters

theta	The estimated parameters.
y	The true values.
w	Weights.

Returns

The dual value.

Implemented in slope::Logistic, slope::Multinomial, slope::Poisson, and slope::Quadratic.

dualPoint() [1/2]

virtual Eigen::MatrixXd slope::Loss::dualPoint ( const Eigen::MatrixXd & eta, const Eigen::MatrixXd & y, bool fit_intercept )

virtual

Constructs a dual candidate from a linear predictor.

When an intercept is fitted, the candidate must satisfy the corresponding zero-sum constraint. Losses with restricted conjugate domains override this method to preserve those domains while enforcing the constraint.

Parameters

eta	Linear predictor.
y	Response.
fit_intercept	Whether the model has an unpenalized intercept.

Returns

A candidate dual point before regularizer scaling.

Reimplemented in slope::Logistic, slope::Multinomial, and slope::Poisson.

dualPoint() [2/2]

virtual Eigen::MatrixXd slope::Loss::dualPoint ( const Eigen::MatrixXd & eta, const Eigen::MatrixXd & y, bool fit_intercept, const Eigen::VectorXd & observation_weights )

virtual

Constructs a dual candidate with weighted intercept stationarity.

Reimplemented in slope::Logistic, slope::Multinomial, and slope::Poisson.

hessianDiagonal()

virtual Eigen::MatrixXd slope::Loss::hessianDiagonal ( const Eigen::MatrixXd & eta )

pure virtual

Calculates the hessian diagonal of the loss function.

This function calculates the hessian diagonal, with respect to the linear predictor eta. \(\frac{\partial^2 L}{\partial \eta^2}\)

Parameters

eta	Linear predictor.

Returns

The residual.

Implemented in slope::Logistic, slope::Multinomial, slope::Poisson, and slope::Quadratic.

inverseLink()

virtual Eigen::MatrixXd slope::Loss::inverseLink ( const Eigen::MatrixXd & eta )

pure virtual

The inverse link function, also known as the mean function.

Parameters

eta

Mean

Returns

The result of applying the inverse link function, which depends on the loss function used.

Implemented in slope::Logistic, slope::Multinomial, slope::Poisson, and slope::Quadratic.

link()

virtual Eigen::MatrixXd slope::Loss::link ( const Eigen::MatrixXd & mu )

pure virtual

The link function.

Parameters

mu

Mean.

Returns

The result of applying the link function, which depends on the loss function used.

Implemented in slope::Logistic, slope::Multinomial, slope::Poisson, and slope::Quadratic.

loss() [1/2]

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

pure virtual

Calculates the loss function.

This function calculates the loss function given the predicted values (eta) and the true values (y).

Parameters

eta	The predicted values.
y	The true values.

Returns

The loss value.

Implemented in slope::Logistic, slope::Multinomial, slope::Poisson, and slope::Quadratic.

loss() [2/2]

virtual double slope::Loss::loss ( const Eigen::MatrixXd & eta, const Eigen::MatrixXd & y, const Eigen::VectorXd & observation_weights )

virtual

Calculates the loss averaged by observation weights.

Reimplemented in slope::Logistic, slope::Multinomial, slope::Poisson, and slope::Quadratic.

predict()

virtual Eigen::MatrixXd slope::Loss::predict ( const Eigen::MatrixXd & eta )

pure virtual

Return predicted response.

Parameters

eta	The linear predictor.

Returns

The predicted response.

Implemented in slope::Logistic, slope::Multinomial, slope::Poisson, and slope::Quadratic.

preprocessResponse()

virtual Eigen::MatrixXd slope::Loss::preprocessResponse ( const Eigen::MatrixXd & y )

pure virtual

Preprocess response.

Parameters

y	The response

Implemented in slope::Logistic, slope::Multinomial, slope::Poisson, and slope::Quadratic.

residual()

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

Calculates the generalized residual.

This function calculates the generalized residual given the linear predictor (eta) and the true values (y). The generalized residual is the same as the gradient of the loss function with respect to the linear predictor (eta).

Parameters

eta	Linear predictor.
y	Response.

Returns

Residual.

updateIntercept()

virtual void slope::Loss::updateIntercept ( Eigen::VectorXd & beta0, const Eigen::MatrixXd & eta, const Eigen::MatrixXd & y )

inlinevirtual

Updates the intercept with a gradient descent update.

Parameters

beta0	The current intercept.
eta	The current linear predictor.
y	The observed counts vector.

Reimplemented in slope::Poisson.

Definition at line 150 of file loss.h.

updateWeightsAndWorkingResponse() [1/2]

virtual void slope::Loss::updateWeightsAndWorkingResponse ( Eigen::MatrixXd & w, Eigen::MatrixXd & z, const Eigen::MatrixXd & eta, const Eigen::MatrixXd & y )

virtual

Updates weights and working response.

This function updates the weights and working response of the quadratic expansion of the loss function.

Parameters

w	Working weights.
z	Working response.
eta	Linear predictor.
y	Response.

Reimplemented in slope::Quadratic.

updateWeightsAndWorkingResponse() [2/2]

virtual void slope::Loss::updateWeightsAndWorkingResponse ( Eigen::MatrixXd & w, Eigen::MatrixXd & z, const Eigen::MatrixXd & eta, const Eigen::MatrixXd & y, const Eigen::VectorXd & observation_weights )

virtual

Updates the IRLS approximation including observation weights.

Reimplemented in slope::Quadratic.

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

• include/slope/losses/loss.h