Hamiltonian Monte Carlo Inference of Marginalized Linear Mixed-Effects Models

TL;DR

This paper introduces an efficient algorithm for marginalizing random effects in linear mixed-effects models, significantly improving Bayesian inference with Hamiltonian Monte Carlo by reducing computational complexity from cubic to linear.

Contribution

We develop a novel linear algebra-based algorithm that simplifies marginalization in LMMs, enhancing HMC inference efficiency and applicability.

Findings

Marginalization improves inference efficiency in LMMs.

Algorithm reduces computational complexity from cubic to linear.

Significant improvements observed in cognitive science models.

Abstract

Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language and then sample via Hamiltonian Monte Carlo (HMC). However, there are many ways a user can transform a model that make inference more or less efficient. In particular, marginalizing some variables can greatly improve inference but is difficult for users to do manually. We develop an algorithm to easily marginalize random effects in LMMs. A naive approach introduces cubic time operations within an inference algorithm like HMC, but we reduce the running time to linear using fast linear algebra techniques. We show that marginalization is always beneficial when applicable and highlight improvements in various models, especially ones from cognitive sciences.