Sketching for Latent Dirichlet-Categorical Models

TL;DR

This paper introduces a novel sketching approach combining count-min sketch and approximate counters to efficiently represent large parameters in latent Dirichlet-Categorical models, enabling scalable Bayesian inference.

Contribution

It proposes a new combination of sketching algorithms for compact parameter representation in Bayesian models, with theoretical analysis of convergence during MCMC inference.

Findings

The combined sketching method is effective for large models.

Sketched MCMC converges to exact posterior as sketch parameters improve.

The approach is applicable to NLP and other large-scale Bayesian inference tasks.

Abstract

Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in memory, and propose more compact representations of parameter values that can be used during inference. We focus on a class of graphical models that we refer to as latent Dirichlet-Categorical models, and show how a combination of two sketching algorithms known as count-min sketch and approximate counters provide an efficient representation for them. We show that this sketch combination -- which, despite having been used before in NLP applications, has not been previously analyzed -- enjoys desirable properties. We prove that for this class of models, when the sketches are used during Markov Chain Monte Carlo inference, the equilibrium of sketched MCMC converges to that of the exact chain as sketch parameters are tuned to reduce the error rate.