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correct likelihod definition

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bobturneruk 2020-06-03 15:52:16 +01:00
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GPy/likelihoods/__init__.py
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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