A Comparison of Bayesian Inference Techniques for Sparse Factor Analysis

TL;DR

This paper compares Bayesian inference methods, MCMC and variational inference, for sparse factor analysis, highlighting the trade-off between computational speed and accuracy in high-dimensional data interpretation.

Contribution

It introduces and compares MCMC and VI algorithms for sparse factor analysis, emphasizing VI's efficiency despite slight accuracy loss.

Findings

VI is significantly faster than MCMC.

VI's accuracy loss is minimal compared to its speed advantage.

The algorithms are validated on simulated and biological data.

Abstract

Dimension reduction algorithms aim to discover latent variables which describe underlying structures in high-dimensional data. Methods such as factor analysis and principal component analysis have the downside of not offering much interpretability of its inferred latent variables. Sparse factor analysis addresses this issue by imposing sparsity on its factor loadings, allowing each latent variable to be related to only a subset of features, thus increasing interpretability. Sparse factor analysis has been used in a wide range of areas including genomics, signal processing, and economics. We compare two Bayesian inference techniques for sparse factor analysis, namely Markov chain Monte Carlo (MCMC), and variational inference (VI). VI is computationally faster than MCMC, at the cost of a loss in accuracy. We derive MCMC and VI algorithms and perform a comparison using both simulated and biological data, demonstrating that the higher computational efficiency of VI is desirable over the small gain in accuracy when using MCMC. Our implementation of MCMC and VI algorithms for sparse factor analysis is available at https://github.com/ysfoo/sparsefactor.