SINW01 | Prof. Gareth Roberts | Optimisation and complexity for Gibbs samplers

Описание: Speaker: Professor Gareth Roberts (University of Warwick)
Date: 5th Jul 2017 - 14:15 to 15:00
Venue: INI Seminar Room 1
Title: Optimisation and complexity for Gibbs samplers for hierarchical and crossed-effect models
Event: (SINW01) Scalable statistical inference
Abstract: We
study the convergence properties of the Gibbs Sampler in the context of
Gaussian hierarchical and crossed-effect models. We develop a novel methodology
based on multi-grid decompositions to derive analytic expressions for the
convergence rates of the algorithm, extending significantly the class of
conditionally Gaussian models amenable to direct analysis. In the hierarchical
context, our work gives a rather complete understanding of the Gibbs Sampler
behaviour for symmetric models (with arbitrary depth), while providing
approximations and bounds for the non-symmetric cases. The theoretical results
give rise to simple and easy-to-implement guidelines to optimise practical
implementations of the Gibbs samplers on such models. While the good
performances of the Gibbs Sampler in hierarchically-structured models is
renowned, the context of crossed-effect models is drastically different. Here
hierarchical centering is not possible and the convergence of commonly
implemented Gibbs Sampler strategies deteriorates as the data-size increases,
resulting in super-linear computational complexity (potentially even quadratic)
in the number of data-points. We show how to leverage the negatively-correlated
structure of crossed-effect models to design easy-to-implement collapsed Gibbs
Samplers whose complexity matches the one of hierarchical scenarios.This is joint work with Giacomo Zanella and Omiros
Papaspiliopoulos.
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