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Title: Kernel methods for nonparametric Bayesian inference of probability densities and point processes
Author: Adams, R. P.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2009
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I propose two new kernel-based models that enable an exact generative procedure: the Gaussian process density sampler (GPDS) for probability density functions, and the sigmoidal Gaussian Cox process (SGCP) for the Poisson process. With generative priors, I show how it is now possible to construct two different kinds of Markov chains for inference in these models. These Markov chains have the desired posterior distribution as their equilibrium distributions, and, despite a parameter space with uncountably many dimensions, require only a finite amount of computation to simulate. The GPDS and SGCP, and the associated inference procedures, are the first kernel-based nonparametric Bayesian methods that allow inference without a finite-dimensional approximation. I also present several additional kernel-based models for data that extend the Gaussian process density sampler and sigmoidal Gaussian Cox process to other situations. The Archipelago model extends the GPDS to address the task of semi-supervised learning, where a flexible density estimate can improve the performance of a classifier when unlabelled data are available. I also generalise the SGCP to enable a nonparametric inhomogeneous Neyman-Scott process, and present a soft-core generalisation of the Matérn repulsive process that similarly allows non-approximate inference via Markov chain Monte Carlo.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available