Discrete Sampling using Semigradient-based Product Mixtures

TL;DR

This paper introduces a new sampling method for discrete probabilistic models that uses semigradient-based product mixtures to enable global moves, improving convergence speed over traditional local Markov chain Monte Carlo algorithms.

Contribution

The paper presents a novel mixture-based sampling strategy leveraging semigradient information to accelerate inference in discrete models, addressing slow convergence issues.

Findings

The proposed sampler accelerates convergence in example models.

Effective in practical models learned from real-world data.

Combines well with existing sampling methods for improved performance.

Abstract

We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and Ising models. Locally-moving Markov chain Monte Carlo algorithms, such as the Gibbs sampler, are commonly used for inference in such models, but their convergence is, at times, prohibitively slow. This is often caused by state-space bottlenecks that greatly hinder the movement of such samplers. We propose a novel sampling strategy that uses a specific mixture of product distributions to propose global moves and, thus, accelerate convergence. Furthermore, we show how to construct such a mixture using semigradient information. We illustrate the effectiveness of combining our sampler with existing ones, both theoretically on an example model, as well as practically on three models learned from real-world data sets.