On Bayesian inferential tasks with infinite-state jump processes: efficient data augmentation

TL;DR

This paper introduces a novel, scalable data augmentation framework for Bayesian inference in infinite-state jump processes, significantly improving efficiency over existing methods and enabling practical inference and clustering in complex models.

Contribution

It develops a tractable, scalable data augmentation approach based on uniformization, extending efficient inference techniques from finite to infinite state spaces in jump processes.

Findings

Enhanced efficiency in inference tasks for infinite-state models

Successful application to real and simulated data sets

Improved scalability over previous methods

Abstract

Advances in sampling schemes for Markov jump processes have recently enabled multiple inferential tasks. However, in statistical and machine learning applications, we often require that these continuous-time models find support on structured and infinite state spaces. In these cases, exact sampling may only be achieved by often inefficient particle filtering procedures, and rapidly augmenting observed datasets remains a significant challenge. Here, we build on the principles of uniformization and present a tractable framework to address this problem, which greatly improves the efficiency of existing state-of-the-art methods commonly used in small finite-state systems, and further scales their use to infinite-state scenarios. We capitalize on the marginal role of variable subsets in a model hierarchy during the process jumps, and describe an algorithm that relies on measurable mappings between pairs of states and carefully designed sets of synthetic jump observations. The proposed method enables the efficient integration of slice sampling techniques and it can overcome the existing computational bottleneck. We offer evidence by means of experiments addressing inference and clustering tasks on both simulated and real data sets.