Statistics Seminars: Towards scalable MCMCs for some latent variable models
6 March 2017 14:00 in CM221
The probabilistic modelling of observed phenomena sometimes require the introduction of (unobserved) latent variables, which may or may not be of direct interest. This is for example the case when a realisation of a Markov chain is observed in noise and one is interested in inferring its transition matrix from the data. In such models inferring the parameters of interest (e.g. the transition matrix above) requires one to incorporate the latent variables in the inference procedure, resulting in practical difficulties. The standard approach to carry out inference in such models consists of integrating the latent variables numerically, most often using Monte Carlo methods. In the toy example above there are as many latent variables as there are observations, making the problem high-dimensional and potentially difficult.
We will show how recent advances in Markov chain Monte Carlo methods, in particular the development of “exact approximations” of the Metropolis-Hastings algorithm (which will be reviewed), can lead to algorithms which scale better than existing solutions.
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