A0197
Title: SOMA: A novel sampler for exchangeable variables
Authors: Nianqiao Ju - Dartmouth College (United States) [presenting]
Yifei Xiong - Purdue University (United States)
Abstract: The problem of sampling exchangeable random variables arises in many Bayesian inference tasks, especially in data imputation given a privatized summary statistic. These permutation-invariant joint distributions often have dependency structures that make sampling challenging. Component-wise sampling strategies, such as Metropolis-within-Gibbs, can mix slowly because they consider only comparing a proposed point with one component at a time. A novel single-offer-multiple-attempts (SOMA) sampler is proposed that is tailored to sampling permutation-invariant distributions. The core intuition of SOMA is that a proposed point unsuitable to replace one component might still be a good candidate to replace some other component in the joint distribution. SOMA first makes a singer offer, and then simultaneously considers attempts to replace each component of the current state with the single offer, before making the final acceptance or rejection decision. An acceptance lower bound of SOMA is provided, and using a coupling method, the convergence rate upper bound of SOMA is derived in the two-dimensional case. Theoretical findings are validated with numerical simulations, including a demonstration of differentially private Bayesian linear regression.
