slope::Multinomial Class Reference

The Multinomial class represents a multinomial logistic regression loss function. More...

#include <multinomial.h>

Inheritance diagram for slope::Multinomial:

Collaboration diagram for slope::Multinomial:

Public Member Functions
double	loss (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y) override
	Calculates the loss for the multinomial loss function.
double	loss (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, const Eigen::VectorXd &observation_weights) override
	Calculates the loss averaged by observation weights.
double	dual (const Eigen::MatrixXd &theta, const Eigen::MatrixXd &y, const Eigen::VectorXd &w) override
	Calculates the dual for the multinomial loss function.
Eigen::MatrixXd	dualPoint (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, bool fit_intercept) override
	Constructs a dual candidate from a linear predictor.
Eigen::MatrixXd	dualPoint (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, bool fit_intercept, const Eigen::VectorXd &observation_weights) override
	Constructs a dual candidate with weighted intercept stationarity.
Eigen::MatrixXd	preprocessResponse (const Eigen::MatrixXd &y) override
	Preprocesses the response for the Multinomial model.
Eigen::MatrixXd	hessianDiagonal (const Eigen::MatrixXd &eta) override
	Calculates the hessian diagonal.
Eigen::MatrixXd	link (const Eigen::MatrixXd &mu) override
	The link function.
Eigen::MatrixXd	inverseLink (const Eigen::MatrixXd &eta) override
	The inverse link function.
Eigen::MatrixXd	predict (const Eigen::MatrixXd &eta) override
	Return predicted response, which is an integer class label based on the predicted probabilities.
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	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 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.
virtual double	deviance (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y, const Eigen::VectorXd &observation_weights)
	Computes deviance averaged by observation weights.

Additional Inherited Members
Protected Member Functions inherited from slope::Loss
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

The Multinomial class represents a multinomial logistic regression loss function.

The multinomial loss function is used for multi-class classification problems. It calculates the loss, dual, residual, and updates weights and working response. It uses the non-redundant formulation of the loss with \(K - 1\) columns in the resulting response matrix.

Definition at line 21 of file multinomial.h.

Constructor & Destructor Documentation

Multinomial()

slope::Multinomial::Multinomial ( )

inlineexplicit

Definition at line 24 of file multinomial.h.

Member Function Documentation

dual()

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

overridevirtual

Calculates the dual for the multinomial loss function.

Parameters

theta	The dual variables (n x m matrix).
y	The true labels (n x m matrix).
w	The weights vector.

Returns

The dual value.

Implements slope::Loss.

dualPoint() [1/2]

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

overridevirtual

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 from slope::Loss.

dualPoint() [2/2]

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

overridevirtual

Constructs a dual candidate with weighted intercept stationarity.

Reimplemented from slope::Loss.

hessianDiagonal()

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

overridevirtual

Calculates the hessian diagonal.

Parameters

eta	Linear predictor

Returns

The hessian diagonal, a matrix of size (n x m)

Implements slope::Loss.

inverseLink()

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

overridevirtual

The inverse link function.

Parameters

eta

Returns

The modified softmax of the linear predictor: \(\frac{e^{\eta}}{1 + \sum_{j=1}^{k} e^{\eta_j}} \)

Implements slope::Loss.

link()

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

overridevirtual

The link function.

Parameters

mu

Mean.

Returns

The result of applying the link function.

Implements slope::Loss.

loss() [1/2]

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

overridevirtual

Calculates the loss for the multinomial loss function.

Parameters

eta	The predicted values (n x m matrix of linear predictors).
y	The true labels (n x m matrix of one-hot encoded class memberships).

Returns

The loss value.

Implements slope::Loss.

loss() [2/2]

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

overridevirtual

Calculates the loss averaged by observation weights.

Reimplemented from slope::Loss.

predict()

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

overridevirtual

Return predicted response, which is an integer class label based on the predicted probabilities.

Parameters

eta	The linear predictor

Returns

The predicted response

Implements slope::Loss.

preprocessResponse()

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

overridevirtual

Preprocesses the response for the Multinomial model.

Parameters

y	Vector of class labels (n x 1). Each entry is an integer representing the class label from 0 to m.

Returns

Matrix of response (n x m)

Implements slope::Loss.

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

• include/slope/losses/multinomial.h