Seminar on Bayesian Computation 

The following schedule is based on Japanese standard time. 

Date: Monday May 13th

Time:  15:00 - 16:00 JST

In person location: ISM D222

Speaker: Kaoru Irie, University of Tokyo

Title: Gibbs sampler for matrix generalized inverse Gaussian distributions

Abstract: Matrix generalized inverse Gaussian (MGIG) distributions are a multivariate extension of the well-known univariate GIG distributions. Typically, the MGIG distributions are obtained as the full conditional posterior distributions of the variance matrix in many multivariate models, such as the location-scale mixture of multivariate normals. Thus, in implementing Markov chain Monte Carlo (MCMC) algorithms for posterior inference, simulation from the MGIG distributions is required. However, an efficient sampling scheme for the MGIG distributions has not been fully developed. In this study, we propose a novel blocked Gibbs sampler for the MGIG distributions based on the Cholesky decomposition. We show that the full conditionals of the entries of the diagonal and unit lower-triangular matrices are univariate GIG and multivariate normal distributions, respectively. Several variants of the Metropolis-Hastings algorithm can also be considered for this problem, but we mathematically prove that the average acceptance rates become extremely low in particular scenarios. We demonstrate the computational efficiency of the proposed Gibbs sampler through simulation studies and data analysis. This is joint work with Yasuyuki Hamura (Kyoto) and Shonosuke Sugasawa (Keio).

参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.

Physical: https://forms.gle/XMAMc4WMCdXXXyKX8

Virtual: https://us06web.zoom.us/meeting/register/tZYucOChrTwuE9H8rMRgZ9a0Yw596TppqGtt

Date: Monday Mar 18th

Time: 13:00 - 14:00 JST

In person location: RIKEN Center for Brain Science, Central Building, C202

Speaker: Omar Chehab, ENSAE-CREST

Title: Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyond

Abstract: Recent research has developed several Monte Carlo methods for estimating the normalization constant (partition function) based on the idea of annealing. This means sampling successively from a path of distributions that interpolate between a tractable "proposal" distribution and the unnormalized "target" distribution. Promi- nent estimators in this family include annealed importance sampling and annealed noise-contrastive estimation (NCE). Such methods hinge on a number of design choices: which estimator to use, which path of distributions to use and whether to use a path at all; so far, there is no definitive theory on which choices are efficient. Here, we evaluate each design choice by the asymptotic estimation error it produces. First, we show that using NCE is more efficient than the importance sampling esti- mator, but in the limit of infinitesimal path steps, the difference vanishes. Second, we find that using the geometric path brings down the estimation error from an exponential to a polynomial function of the parameter distance between the target and proposal distributions. Third, we find that the arithmetic path, while rarely used, can offer optimality properties over the universally-used geometric path. In fact, in a particular limit, the optimal path is arithmetic. Based on this theory, we finally propose a two-step estimator to approximate the optimal path in an efficient way.

参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.

Physical: https://forms.gle/7nhDTSeJokNdVx8a9

Virtual: https://us06web.zoom.us/meeting/register/tZ0td-GrrjorHt0YpnLKQuqPLxd3lsFgopFb