From e0304056f95de8922fce72b2a7ddfcd9bb4916ce Mon Sep 17 00:00:00 2001 From: bobturneruk Date: Wed, 3 Jun 2020 15:52:16 +0100 Subject: [PATCH] correct likelihod definition --- GPy/likelihoods/__init__.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/GPy/likelihoods/__init__.py b/GPy/likelihoods/__init__.py index 606a5167..975abc88 100644 --- a/GPy/likelihoods/__init__.py +++ b/GPy/likelihoods/__init__.py @@ -2,7 +2,7 @@ Introduction ^^^^^^^^^^^^ -'Likelihood' in this context is a measure of how well a model *f* predicts a dataset *y*. The importance of likelihoods in Gaussian Processes is in determining the 'best' values of kernel and noise hyperparamters to relate known, observed and unobserved data. The purpose of optimizing a model (e.g. :py:class:`GPy.models.GPRegression`) is to determine the 'best' hyperparameters i.e. those that minimize negative log marginal likelihood. +The likelihood is :math:`p(y|f,X)` which is how well we will predict target values given inputs :math:`X` and our latent function :math:`f` (:math:`y` without noise). Marginal likelihood :math:`p(y|X)`, is the same as likelihood except we marginalize out the model :math:`f`. The importance of likelihoods in Gaussian Processes is in determining the 'best' values of kernel and noise hyperparamters to relate known, observed and unobserved data. The purpose of optimizing a model (e.g. :py:class:`GPy.models.GPRegression`) is to determine the 'best' hyperparameters i.e. those that minimize negative log marginal likelihood. .. inheritance-diagram:: GPy.likelihoods.likelihood GPy.likelihoods.mixed_noise.MixedNoise :top-classes: GPy.core.parameterization.parameterized.Parameterized