Bayesian and L1 Approaches to Sparse Unsupervised Learning

TL;DR

This paper compares L1 regularisation and Bayesian spike-and-slab methods for sparse unsupervised learning, showing Bayesian approaches often outperform L1 in predictive accuracy and generalisation.

Contribution

It introduces Bayesian spike-and-slab factor models that better induce sparsity and account for uncertainty, outperforming L1 methods in various datasets.

Findings

Bayesian spike-and-slab models outperform L1 minimisation in predictive tasks.

Bayesian methods better handle uncertainty and avoid unnecessary shrinkage.

L1 regularisation often underperforms in generalisation compared to Bayesian approaches.

Abstract

The use of L1 regularisation for sparse learning has generated immense research interest, with successful application in such diverse areas as signal acquisition, image coding, genomics and collaborative filtering. While existing work highlights the many advantages of L1 methods, in this paper we find that L1 regularisation often dramatically underperforms in terms of predictive performance when compared with other methods for inferring sparsity. We focus on unsupervised latent variable models, and develop L1 minimising factor models, Bayesian variants of "L1", and Bayesian models with a stronger L0-like sparsity induced through spike-and-slab distributions. These spike-and-slab Bayesian factor models encourage sparsity while accounting for uncertainty in a principled manner and avoiding unnecessary shrinkage of non-zero values. We demonstrate on a number of data sets that in practice spike-and-slab Bayesian methods outperform L1 minimisation, even on a computational budget. We thus highlight the need to re-assess the wide use of L1 methods in sparsity-reliant applications, particularly when we care about generalising to previously unseen data, and provide an alternative that, over many varying conditions, provides improved generalisation performance.