Scalable inference for crossed random effects models

TL;DR

This paper investigates the scalability issues of Gibbs samplers in crossed random effects models and proposes a modified, provably scalable collapsed Gibbs sampler that outperforms existing algorithms.

Contribution

It introduces a simple modification to the Gibbs sampler, making it scalable for complex crossed random effects models, with theoretical guarantees and practical improvements.

Findings

Plain Gibbs sampler is not scalable for certain designs.

The proposed collapsed Gibbs sampler is provably scalable.

The new sampler outperforms existing algorithms in experiments.

Abstract

We analyze the complexity of Gibbs samplers for inference in crossed random effect models used in modern analysis of variance. We demonstrate that for certain designs the plain vanilla Gibbs sampler is not scalable, in the sense that its complexity is worse than proportional to the number of parameters and data. We thus propose a simple modification leading to a collapsed Gibbs sampler that is provably scalable. Although our theory requires some balancedness assumptions on the data designs, we demonstrate in simulated and real datasets that the rates it predicts match remarkably the correct rates in cases where the assumptions are violated. We also show that the collapsed Gibbs sampler, extended to sample further unknown hyperparameters, outperforms significantly alternative state of the art algorithms.