A Review of Bayesian Methods for Infinite Factorisations

TL;DR

This paper reviews Bayesian infinite factor models, highlighting their ability to adaptively determine the number of latent factors using shrinkage priors and adaptive MCMC inference, with a discussion on their properties and trade-offs.

Contribution

It provides a comprehensive overview of Bayesian infinite factor models, emphasizing their adaptive dimension determination and comparing their advantages and limitations.

Findings

Infinite factor models automatically adapt the number of factors based on data.

Shrinkage priors effectively penalize increasing factor dimensionality.

Discussion of the properties and comparative advantages of these models.

Abstract

Defining the number of latent factors has been one of the most challenging problems in factor analysis. Infinite factor models offer a solution to this problem by applying increasing shrinkage on the columns of factor loading matrices, thus penalising increasing factor dimensionality. The adaptive MCMC algorithms used for inference in such models allow to defer the dimension of the latent factor space automatically based on the data. This paper presents an overview of Bayesian models for infinite factorisations with some discussion on the properties of such models as well as their comparative advantages and drawbacks.