arXiv subjects

Jacob Vorstrup Goldman

Publications and source records attributed to Jacob Vorstrup Goldman.

3 recordsLinked to original sources

arXiv2021

Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state space models

We propose a novel blocked version of the continuous-time bouncy particle sampler of [Bouchard-Côté et al., 2018] which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state space models [Singh et al., 2017] and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. The new algorithms are particularly efficient for latent state inference in high-dimensional state space models, where blocking in both space and time is necessary to avoid degeneracy of MCMC. The efficiency of our blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. [2010], is illustrated numerically for both simulated data and a challenging real-world financial dataset.

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arXiv2021

Gradient-Based Markov Chain Monte Carlo for Bayesian Inference With Non-Differentiable Priors

The use of non-differentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state of the art methods are approximate in the sense that they replace the posterior with a smooth approximation via Moreau-Yosida envelopes, and apply gradient-based discretized diffusions to sample from the resulting distribution. We characterize the error of the Moreau-Yosida approximation and propose a novel implementation using underdamped Langevin dynamics. In misson-critical cases, however, replacing the posterior with an approximation may not be a viable option. Instead, we show that Piecewise-Deterministic Markov Processes (PDMP) can be utilized for exact posterior inference from distributions satisfying almost everywhere differentiability. Furthermore, in contrast with diffusion-based methods, the suggested PDMP-based samplers place no assumptions on the prior shape, nor require access to a computationally cheap proximal operator, and consequently have a much broader scope of application. Through detailed numerical examples, including a non-differentiable circular distribution and a non-convex genomics model, we elucidate the relative strengths of these sampling methods on problems of moderate to high dimensions, underlining the benefits of PDMP-based methods when accurate sampling is decisive.

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arXiv2019

Accelerated Sampling on Discrete Spaces with Non-Reversible Markov Processes

We consider the task of MCMC sampling from a distribution defined on a discrete space. Building on recent insights provided in [Zan19], we devise a class of efficient continuous-time, non-reversible algorithms which make active use of the structure of the underlying space. Particular emphasis is placed on how symmetries and other group-theoretic notions can be used to improve exploration of the space. We test our algorithms on a range of examples from statistics, computational physics, machine learning, and cryptography, which show improvement on alternative algorithms. We provide practical recommendations on how to design and implement these algorithms, and close with remarks on the outlook for both discrete sampling and continuous-time Monte Carlo more broadly.

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