smile.glm.model.Model Maven / Gradle / Ivy
/*
* Copyright (c) 2010-2021 Haifeng Li. All rights reserved.
*
* Smile is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Smile is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Smile. If not, see
* - An exponential family of probability distributions.
* - A linear predictor.
* - A link function provides the relationship between the linear
* predictor and the mean of the distribution function.
*
* This class specifies the distribution and link function in the model.
*
* An overdispersed exponential family of distributions is a generalization
* of an exponential family and the exponential dispersion model of
* distributions and includes those families of probability distributions,
* parameterized by θ and τ. The parameter θ is related
* to the mean of the distribution. The dispersion parameter τ typically
* is known and is usually related to the variance of the distribution.
*
* There are many commonly used link functions, and their choice is informed
* by several considerations. There is always a well-defined canonical link
* function which is derived from the exponential of the response's density
* function. However, in some cases it makes sense to try to match the domain
* of the link function to the range of the distribution function's mean,
* or use a non-canonical link function for algorithmic purposes.
*
* @author Haifeng Li
*/
public interface Model extends Serializable {
/**
* The link function. For the most common distributions, the mean μ
* is one of the parameters in the standard form of the distribution's
* density function, and then the link function maps the density
* function into its canonical form.
*
* @param mu the mean of the distribution function.
* @return the linear predictor.
*/
double link(double mu);
/**
* The inverse of link function (aka the mean function).
*
* @param eta the linear predictor. The linear predictor is the quantity
* which incorporates the independent variables into the model.
* @return the mean.
*/
double invlink(double eta);
/**
* The derivative of link function.
*
* @param mu the mean of the distribution function.
* @return the derivative of link function.
*/
double dlink(double mu);
/**
* The variance function.
*
* @param mu the mean of the distribution function.
* @return the variance function value.
*/
double variance(double mu);
/**
* The deviance function.
*
* @param y the responsible variable.
* @param mu the mean of the distribution function.
* @param residuals the residuals.
* @return the deviance function value.
*/
double deviance(double[] y, double[] mu, double[] residuals);
/**
* The NULL deviance function.
*
* @param y the responsible variable.
* @param mu the mean of the distribution function.
* @return the null deviance function value.
*/
double nullDeviance(double[] y, double mu);
/**
* The log-likelihood function.
* @param y the responsible variable.
* @param mu the mean of the distribution function.
* @return the log-likelihood.
*/
double logLikelihood(double[] y, double[] mu);
/**
* The function to estimates the starting value of mean given y.
* @param y the responsible variable.
* @return the starting value of mean.
*/
double mustart(double y);
}