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"""
Link functions used in GLM
"""
# Author: Christian Lorentzen <lorentzen.ch@googlemail.com>
# License: BSD 3 clause
from abc import ABCMeta, abstractmethod
import numpy as np
from scipy.special import expit, logit
class BaseLink(metaclass=ABCMeta):
"""Abstract base class for Link functions."""
@abstractmethod
def __call__(self, y_pred):
"""Compute the link function g(y_pred).
The link function links the mean y_pred=E[Y] to the so called linear
predictor (X*w), i.e. g(y_pred) = linear predictor.
Parameters
----------
y_pred : array of shape (n_samples,)
Usually the (predicted) mean.
"""
@abstractmethod
def derivative(self, y_pred):
"""Compute the derivative of the link g'(y_pred).
Parameters
----------
y_pred : array of shape (n_samples,)
Usually the (predicted) mean.
"""
@abstractmethod
def inverse(self, lin_pred):
"""Compute the inverse link function h(lin_pred).
Gives the inverse relationship between linear predictor and the mean
y_pred=E[Y], i.e. h(linear predictor) = y_pred.
Parameters
----------
lin_pred : array of shape (n_samples,)
Usually the (fitted) linear predictor.
"""
@abstractmethod
def inverse_derivative(self, lin_pred):
"""Compute the derivative of the inverse link function h'(lin_pred).
Parameters
----------
lin_pred : array of shape (n_samples,)
Usually the (fitted) linear predictor.
"""
class IdentityLink(BaseLink):
"""The identity link function g(x)=x."""
def __call__(self, y_pred):
return y_pred
def derivative(self, y_pred):
return np.ones_like(y_pred)
def inverse(self, lin_pred):
return lin_pred
def inverse_derivative(self, lin_pred):
return np.ones_like(lin_pred)
class LogLink(BaseLink):
"""The log link function g(x)=log(x)."""
def __call__(self, y_pred):
return np.log(y_pred)
def derivative(self, y_pred):
return 1 / y_pred
def inverse(self, lin_pred):
return np.exp(lin_pred)
def inverse_derivative(self, lin_pred):
return np.exp(lin_pred)
class LogitLink(BaseLink):
"""The logit link function g(x)=logit(x)."""
def __call__(self, y_pred):
return logit(y_pred)
def derivative(self, y_pred):
return 1 / (y_pred * (1 - y_pred))
def inverse(self, lin_pred):
return expit(lin_pred)
def inverse_derivative(self, lin_pred):
ep = expit(lin_pred)
return ep * (1 - ep)
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