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	residual (const Eigen::MatrixXd &eta, const Eigen::MatrixXd &y) override
	Calculates the residual (negative gradient) for the Poisson regression.

void	updateWeightsAndWorkingResponse (Eigen::VectorXd &w, Eigen::VectorXd &z, const Eigen::VectorXd &eta, const Eigen::VectorXd &y) override
	Updates the weights and working response for IRLS (Iteratively Reweighted Least Squares).

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.

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.

Definition at line 13 of file poisson.cpp.

◆ 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.

Definition at line 69 of file poisson.cpp.

◆ link()

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

overridevirtual

The link function.

Parameters

mu Mean.

Returns: \( \log(\mu) \)

Implements slope::Loss.

Definition at line 63 of file poisson.cpp.

◆ 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.

Definition at line 7 of file poisson.cpp.

◆ 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.

Definition at line 75 of file poisson.cpp.

◆ 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.

Definition at line 41 of file poisson.cpp.

◆ residual()

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

overridevirtual

Calculates the residual (negative gradient) for the Poisson regression.

Parameters

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

Returns: The residual vector: \(e^{\eta} - y\)

Implements slope::Loss.

Definition at line 25 of file poisson.cpp.

◆ 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.

Definition at line 51 of file poisson.cpp.

◆ updateWeightsAndWorkingResponse()

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

overridevirtual

Updates the weights and working response for IRLS (Iteratively Reweighted Least Squares).

Parameters

w	The weights vector: \(w = e^{\eta}\)
z	The working response vector: \(z = \eta + (y - e^{\eta})/e^{\eta}\)
eta	The current linear predictor
y	The observed counts vector

Implements slope::Loss.

Definition at line 31 of file poisson.cpp.

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

src/slope/losses/poisson.h
src/slope/losses/poisson.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Poisson()

Member Function Documentation

◆ dual()

◆ inverseLink()

◆ link()

◆ loss()

◆ predict()

◆ preprocessResponse()

◆ residual()

◆ updateIntercept()

◆ updateWeightsAndWorkingResponse()