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)
	Calculates the loss for the multinomial loss function.
double	dual (const Eigen::MatrixXd &theta, const Eigen::MatrixXd &y, const Eigen::VectorXd &w)
	Calculates the dual for the multinomial loss function.
Eigen::MatrixXd	residual (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y)
	Calculates the residual for the multinomial loss function.
Eigen::MatrixXd	preprocessResponse (const Eigen::MatrixXd &y)
	Preprocesses the response for the Multinomial model.
void	updateWeightsAndWorkingResponse (Eigen::VectorXd &w, Eigen::VectorXd &z, const Eigen::VectorXd &eta, const Eigen::VectorXd &y)
	Updates the weights and working response for the multinomial loss function. Currently not implemented since there is no coordinate descent solver for the multinomial logistic regression loss.
Eigen::MatrixXd	link (const Eigen::MatrixXd &mu)
	The link function.
Eigen::MatrixXd	inverseLink (const Eigen::MatrixXd &eta)
	The inverse link function, also known as the mean function.
Eigen::MatrixXd	predict (const Eigen::MatrixXd &eta)
	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.
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

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. Assumes the response y is a one-hot encoded matrix where each row sums to 1.

Definition at line 20 of file multinomial.h.

Constructor & Destructor Documentation

Multinomial()

slope::Multinomial::Multinomial ( )

inlineexplicit

Definition at line 23 of file multinomial.h.

Member Function Documentation

dual()

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

virtual

Calculates the dual for the multinomial loss function.

Parameters

theta	The dual variables (n x k matrix).
y	The true labels (n x k matrix of one-hot encoded class memberships).
w	The weights vector.

Returns

The dual value.

Implements slope::Loss.

Definition at line 24 of file multinomial.cpp.

inverseLink()

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

virtual

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

Parameters

eta

Returns

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

Implements slope::Loss.

Definition at line 106 of file multinomial.cpp.

link()

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

virtual

The link function.

Parameters

mu

Mean.

Returns

The result of applying the link function.

Implements slope::Loss.

Definition at line 98 of file multinomial.cpp.

loss()

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

virtual

Calculates the loss for the multinomial loss function.

Parameters

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

Returns

The loss value.

Implements slope::Loss.

Definition at line 10 of file multinomial.cpp.

predict()

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

virtual

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.

Definition at line 112 of file multinomial.cpp.

preprocessResponse()

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

virtual

Preprocesses the response for the Multinomial model.

Parameters

y	Predicted values vector (n x 1) of integer class labels

Returns

Matrix of response (n x 1)

Implements slope::Loss.

Definition at line 40 of file multinomial.cpp.

residual()

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

virtual

Calculates the residual for the multinomial loss function.

Parameters

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

Returns

The residual matrix (n x k).

Implements slope::Loss.

Definition at line 34 of file multinomial.cpp.

updateWeightsAndWorkingResponse()

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

virtual

Updates the weights and working response for the multinomial loss function. Currently not implemented since there is no coordinate descent solver for the multinomial logistic regression loss.

Parameters

w	The weights vector.
z	The working response vector.
eta	The predicted values (n x k matrix of linear predictors).
y	The true labels (n x k matrix of one-hot encoded class memberships).

Implements slope::Loss.

Definition at line 89 of file multinomial.cpp.

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

• src/slope/losses/multinomial.h
• src/slope/losses/multinomial.cpp