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