slope::Poisson Class Reference

The Poisson class represents a Poisson regression loss function. More...

#include <poisson.h>

Inheritance diagram for slope::Poisson:

Collaboration diagram for slope::Poisson:

Public Member Functions
double	loss (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y) override
	Calculates the negative log-likelihood loss for the Poisson regression.
double	dual (const Eigen::MatrixXd &theta, const Eigen::MatrixXd &y, const Eigen::VectorXd &w) override
	Calculates the Fenchel conjugate (dual) of the Poisson loss.
Eigen::MatrixXd	hessianDiagonal (const Eigen::MatrixXd &eta) override
	Calculates hessian diagonal.
Eigen::MatrixXd	preprocessResponse (const Eigen::MatrixXd &y) override
	Preprocesses the response for the Poisson model.
void	updateIntercept (Eigen::VectorXd &beta0, const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y) override
	Updates the intercept with a gradient descent update. Unlike the Quadratic and Logistic cases, the Poisson regression intercept update is not quite as simple since the gradient is not Lipschitz continuous. Instead we use a backtracking line search here.
Eigen::MatrixXd	link (const Eigen::MatrixXd &mu) override
	The link function.
Eigen::MatrixXd	inverseLink (const Eigen::MatrixXd &eta) override
	The inverse link function, also known as the mean function.
Eigen::MatrixXd	predict (const Eigen::MatrixXd &eta) override
	Return predicted response, that is 0 or 1 depending 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 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 Poisson class represents a Poisson regression loss function.

The Poisson regression loss function is used for modeling count data. It assumes the response variable follows a Poisson distribution. The log-likelihood for a single observation is:

\[ \ell(y_i|\eta_i) = y_i\eta_i - e^{\eta_i} - \log(y_i!) \]

where \(\eta_i\) is the linear predictor and \(y_i\) is the observed count.

Definition at line 24 of file poisson.h.

Constructor & Destructor Documentation

Poisson()

slope::Poisson::Poisson ( )

inlineexplicit

Definition at line 28 of file poisson.h.

Member Function Documentation

dual()

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

overridevirtual

Calculates the Fenchel conjugate (dual) of the Poisson loss.

Parameters

theta	The dual variables
y	The observed counts vector
w	The weights vector

Returns

The dual objective value

Implements slope::Loss.

hessianDiagonal()

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

overridevirtual

Calculates hessian diagonal.

Parameters

eta	Linear predictor

Returns

A matrix of ones (n x m)

Implements slope::Loss.

inverseLink()

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

overridevirtual

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

Parameters

eta	Linear predictor

Returns

\( \exp(\eta) \)

Implements slope::Loss.

link()

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

overridevirtual

The link function.

Parameters

mu

Mean.

Returns

\( \log(\mu) \)

Implements slope::Loss.

loss()

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

overridevirtual

Calculates the negative log-likelihood loss for the Poisson regression.

Parameters

eta	The linear predictor vector \(\eta\)
y	The observed counts vector \(y\)

Returns

The negative log-likelihood: \(-\sum_i(y_i\eta_i - e^{\eta_i})\) (ignoring constant terms)

Implements slope::Loss.

predict()

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

overridevirtual

Return predicted response, that is 0 or 1 depending on the predicted probabilities.

Parameters

eta	The linear predictor

Returns

The predicted response, which is the same as the inverse link in the case of the Poisson loss.

Implements slope::Loss.

preprocessResponse()

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

overridevirtual

Preprocesses the response for the Poisson model.

Checks if the response is non-negative and throws an error otherwise.

Parameters

y	Predicted values vector (n x 1)

Returns

Vector of residuals (n x 1)

Implements slope::Loss.

updateIntercept()

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

overridevirtual

Updates the intercept with a gradient descent update. Unlike the Quadratic and Logistic cases, the Poisson regression intercept update is not quite as simple since the gradient is not Lipschitz continuous. Instead we use a backtracking line search here.

Parameters

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

Reimplemented from slope::Loss.

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

• include/slope/losses/poisson.h