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latent function inference intro and format

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bobturneruk 2020-06-18 09:36:24 +01:00
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GPy/inference/latent_function_inference/__init__.py
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# Copyright (c) 2012-2014, Max Zwiessele, James Hensman
# Licensed under the BSD 3-clause license (see LICENSE.txt)
__doc__ = """
"""
Introduction
^^^^^^^^^^^^
Certain :py:class:`GPy.models` can be instanciated with an `inference_method`. This submodule contains objects that can be assigned to `inference_method`.
Inference over Gaussian process latent functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
In all our GP models, the consistency propery means that we have a Gaussian
prior over a finite set of points f. This prior is
In all our GP models, the consistency property means that we have a Gaussian
prior over a finite set of points f. This prior is:
math:: N(f | 0, K)
.. math::
N(f | 0, K)
where K is the kernel matrix.
where :math:`K` is the kernel matrix.
We also have a likelihood (see GPy.likelihoods) which defines how the data are
related to the latent function: p(y | f). If the likelihood is also a Gaussian,
the inference over f is tractable (see exact_gaussian_inference.py).
We also have a likelihood (see :py:class:`GPy.likelihoods`) which defines how the data are
related to the latent function: :math:`p(y | f)`. If the likelihood is also a Gaussian,
the inference over :math:`f` is tractable (see :py:class:`GPy.inference.latent_function_inference.exact_gaussian_inference`).
If the likelihood object is something other than Gaussian, then exact inference
is not tractable. We then resort to a Laplace approximation (laplace.py) or
expectation propagation (ep.py).
is not tractable. We then resort to a Laplace approximation (:py:class:`GPy.inference.latent_function_inference.laplace`) or
expectation propagation (:py:class:`GPy.inference.latent_function_inference.expectation_propagation`).
The inference methods return a
:class:`~GPy.inference.latent_function_inference.posterior.Posterior`