Double seminar: Tore S. Kleppe (University of Stavanger) & Christopher Nemeth (Lancaster University)
Tore S. Kleppe (Department of Mathematics and Physics, University of Stavanger) and Christopher Nemeth (Department of Mathematics and Statistics, Lancaster University) will both give a talk on November 30th, at 10:15 and 11:15, respectively, in the Seminar Room 819, Niels Henrik Abels hus, 8th floor.
TORE S. KLEPPE
Title: Dynamically rescaled Hamiltonian Monte Carlo for Bayesian Hierarchical Models
Abstract: Dynamically rescaled Hamiltonian Monte Carlo (DRHMC) is introduced as a computationally fast and easily implemented method for performing full Bayesian analysis in hierarchical statistical models. The method relies on introducing a modified parameterisation so that the re-parameterised target distribution has close to constant scaling properties, and thus is easily sampled using standard (Euclidian metric) Hamiltonian Monte Carlo. Provided that the parameterisations of the conditional distributions specifying the hierarchical model are "constant information parameterisations" (CIP), the relation between the modified- and original parameterisation is bijective, explicitly computed and admit exploitation of sparsity in the numerical linear algebra involved. CIPs for a large catalogue of statistical models are presented, and from the catalogue, it is clear that many CIPs are currently routinely used in statistical computing. A relation between the proposed methodology and a class of explicitly integrated Riemann manifold Hamiltonian Monte Carlo methods is discussed. The methodology is illustrated on several example models, including a model for inflation rates with multiple levels of non-linearly dependent latent variables.
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Title: Are Monte Carlo methods dead?
Abstract: Monte Carlo methods, and in particular Markov chain Monte Carlo techniques, have been the gold standard computational tool for Bayesian modelling over the past 30 years. These algorithms can be applied in general settings, from identifying traits in phylogenetic trees to detecting Earth-like planets in distant solar systems, their supporting theoretical guarantees have led them to be widely used by scientists and industry practitioners alike. However, a significant drawback is that traditional Monte Carlo algorithms scale poorly with large datasets, leading to a computational cost that grows at least proportionally with the data size. This leads to a prohibitive cost for modern-day machine learning and data science applications and has led practitioners towards scalable approximate alternatives, such as variational methods, which have no theoretical guarantees on the resulting approximation error. In this talk, I'll discuss some recent advances in scalable Monte Carlo methods which maintain the favourable theoretical properties of standard Monte Carlo methods, but which are generalisable and suitable for real-world datasets and industrial-scale models.
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