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Activity Number: 64 - Computational Advances in Bayesian Inference
Type: Contributed
Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #320756
Title: Bounding Wasserstein Distance with Couplings
Author(s): Niloy Biswas* and Lester Mackey
Companies: Harvard University and Microsoft Research New England
Keywords: Markov chain Monte Carlo; Stochastic gradients; Approximate Markov chain Monte Carlo; Variational inference; Wasserstein distance; Unadjusted Langevin Algorithm

Markov chain Monte Carlo (MCMC) provides asymptotically consistent estimates of intractable posterior expectations as the number of iterations tends to infinity. However, in large data applications, MCMC can be computationally expensive per iteration. This has catalyzed interest in sampling methods such as approximate MCMC, which trade off asymptotic consistency for improved computational speed. In this article, we propose estimators based on couplings of Markov chains to assess the quality of such asymptotically biased sampling methods. The estimators give empirical upper bounds of the Wassertein distance between the limiting distribution of the asymptotically biased sampling method and the original target distribution of interest. We establish theoretical guarantees for our upper bounds and show that our estimators can remain effective in high dimensions. We apply our quality measures to stochastic gradient MCMC, variational Bayes, and Laplace approximations for tall data and to approximate MCMC for Bayesian logistic regression in 4500 dimensions and Bayesian linear regression in 50000 dimensions.

Authors who are presenting talks have a * after their name.

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