Sampling on Discrete Spaces with Temporal Point Processes

TL;DR

This paper introduces a novel temporal point process-based sampling method for discrete distributions, demonstrating improved performance over existing birth-death and Zanella processes in simulations.

Contribution

It constructs a multivariate temporal point process capable of sampling from any target multivariate count distribution with downward-closed support, with applications to neural network models.

Findings

Sampler outperforms birth-death processes in simulations.

Frequent outperforming of Zanella processes in effective sample size.

Simulation results show improved efficiency normalized by CPU time.

Abstract

Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with downward-closed support, a multivariate temporal point process whose event-count vector in a fixed-length sliding window converges in distribution to the target as time tends to infinity. Structured as a system of potentially coupled infinite-server queues with deterministic service times, the sampler exhibits a discrete form of momentum that suppresses random-walk behaviour. The admissible families of processes permit both reversible and non-reversible dynamics. As an application, we derive a recurrent stochastic neural network whose dynamics implement sampling-based computation and exhibit some biologically plausible features, including relative refractory periods and oscillations. The introduction of auxiliary randomness reduces the sampler to a birth-death process, establishing the latter as a degenerate case with the same limiting distribution. In simulations on 63 target distributions, our sampler always outperforms these birth-death processes and frequently outperforms Zanella processes in multivariate effective sample size, with further gains when normalized by CPU time.