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Approximation methods for latent variable models

Parsons, S; (2016) Approximation methods for latent variable models. Doctoral thesis , UCL (University College London). Green open access

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Modern statistical models are often intractable, and approximation methods can be required to perform inference on them. Many different methods can be employed in most contexts, but not all are fully understood. The current thesis is an investigation into the use of various approximation methods for performing inference on latent variable models. Composite likelihoods are used as surrogates for the likelihood function of state space models (SSM). In chapter 3, variational approximations to their evaluation are investigated, and the interaction of biases as composite structure changes is observed. The bias effect of increasing the block size in composite likelihoods is found to balance the statistical benefit of including more data in each component. Predictions and smoothing estimates are made using approximate Expectation- Maximisation (EM) techniques. Variational EM estimators are found to produce predictions and smoothing estimates of a lesser quality than stochastic EM estimators, but at a massively reduced computational cost. Surrogate latent marginals are introduced in chapter 4 into a non-stationary SSM with i.i.d. replicates. They are cheap to compute, and break functional dependencies on parameters for previous time points, giving estimation algorithms linear computational complexity. Gaussian variational approximations are integrated with the surrogate marginals to produce an approximate EM algorithm. Using these Gaussians as proposal distributions in importance sampling is found to offer a positive trade-off in terms of the accuracy of predictions and smoothing estimates made using estimators. A cheap to compute model based hierarchical clustering algorithm is proposed in chapter 5. A cluster dissimilarity measure based on method of moments estimators is used to avoid likelihood function evaluation. Computation time for hierarchical clustering sequences is further reduced with the introduction of short-lists that are linear in the number of clusters at each iteration. The resulting clustering sequences are found to have plausible characteristics in both real and synthetic datasets.

Type: Thesis (Doctoral)
Title: Approximation methods for latent variable models
Event: UCL (University College London)
Open access status: An open access version is available from UCL Discovery
Language: English
Keywords: Variational approximations, composite likelihoods, state space models, surrogate marginal distributions, model based cluster dissimilarity, method of moments
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1513250
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