Scalable Gaussian process inference using variational methods

cam.supervisorGhahramani, Zoubin
dc.contributor.authorMatthews, Alexander Graeme de Garis
dc.contributor.orcidMatthews, Alexander Graeme de Garis [0000-0002-8552-3526]
dc.description.abstractGaussian processes can be used as priors on functions. The need for a flexible, principled, probabilistic model of functional relations is common in practice. Consequently, such an approach is demonstrably useful in a large variety of applications. Two challenges of Gaussian process modelling are often encountered. These are dealing with the adverse scaling with the number of data points and the lack of closed form posteriors when the likelihood is non-Gaussian. In this thesis, we study variational inference as a framework for meeting these challenges. An introductory chapter motivates the use of stochastic processes as priors, with a particular focus on Gaussian process modelling. A section on variational inference reviews the general definition of Kullback-Leibler divergence. The concept of prior conditional matching that is used throughout the thesis is contrasted to classical approaches to obtaining tractable variational approximating families. Various theoretical issues arising from the application of variational inference to the infinite dimensional Gaussian process setting are settled decisively. From this theory we are able to give a new argument for existing approaches to variational regression that settles debate about their applicability. This view on these methods justifies the principled extensions found in the rest of the work. The case of scalable Gaussian process classification is studied, both for its own merits and as a case study for non-Gaussian likelihoods in general. Using the resulting algorithms we find credible results on datasets of a scale and complexity that was not possible before our work. An extension to include Bayesian priors on model hyperparameters is studied alongside a new inference method that combines the benefits of variational sparsity and MCMC methods. The utility of such an approach is shown on a variety of example modelling tasks. We describe GPflow, a new Gaussian process software library that uses TensorFlow. Implementations of the variational algorithms discussed in the rest of the thesis are included as part of the software. We discuss the benefits of GPflow when compared to other similar software. Increased computational speed is demonstrated in relevant, timed, experimental comparisons.
dc.description.sponsorshipEPSRC grant EP/I036575/1
dc.publisher.collegeDarwin College
dc.publisher.institutionUniversity of Cambridge
dc.rightsAll rights reserved
dc.rightsAll Rights Reserveden
dc.rights.generalIncluded TensorFlow source file has the Apache 2.0 license. Copyright is held by Google Inc. The license header reads: /* Copyright 2015 Google Inc. All Rights Reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. TensorFlow is a trademark of Google Inc.
dc.subjectGaussian process
dc.subjectVariational inference
dc.subjectMachine learning
dc.subjectBayesian inference
dc.titleScalable Gaussian process inference using variational methods
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.type.qualificationtitlePhD in Engineering
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