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General Bayesian inference schemes in infinite mixture models

Lomelí-García, MD; (2017) General Bayesian inference schemes in infinite mixture models. Doctoral thesis , UCL (University College London). Green open access

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Abstract

Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its inherent complexity. One way to do so is through compositional models, which are formed by combining blocks or components consisting of simpler models. One can increase the complexity of the compositional model by either stacking more blocks or by using a not-so-simple model as a building block. This thesis is an example of the latter. One first aim is to expand the choice of Bayesian nonparametric (BNP) blocks for constructing tractable compositional models. So far, most of the models that have a Bayesian nonparametric component use either a Dirichlet Process or a Pitman–Yor process because of the availability of tractable and compact representations. This thesis shows how to overcome certain intractabilities in order to obtain analogous compact representations for the very wide class of Poisson–Kingman priors which includes the Dirichlet and Pitman–Yor processes. A major impediment to the widespread use of Bayesian nonparametric building blocks is that inference is often costly, intractable or difficult to carry out. This is an active research area since dealing with the model’s infinite dimensional component forbids the direct use of standard simulation-based methods. The main contribution of this thesis is a variety of inference schemes that tackle this problem: Markov chain Monte Carlo and Sequential Monte Carlo methods, which are exact inference methods since they target the true posterior. The contributions of this thesis, in a larger context, provide general purpose exact inference schemes in the flavour or probabilistic programming: the user is able to choose from a variety of models, focusing only on the modelling part. We show how if the wide enough class of Poisson–Kingman priors is used as one of our blocks, this objective is achieved.

Type: Thesis (Doctoral)
Title: General Bayesian inference schemes in infinite mixture models
Event: UCL (University College London)
Open access status: An open access version is available from UCL Discovery
Language: English
UCL classification: UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit
URI: http://discovery.ucl.ac.uk/id/eprint/1537554
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