Generalized infinite factorization models
arXiv:2103.10333 · doi:10.1093/biomet/asab056
Abstract
Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to infer the relative impact of the different components as well as the number of components. A popular idea is to include infinitely many components having impact decreasing with the component index. This article is motivated by two limitations of existing methods: (1) lack of careful consideration of the within component sparsity structure; and (2) no accommodation for grouped variables and other non-exchangeable structures. We propose a general class of infinite factorization models that address these limitations. Theoretical support is provided, practical gains are shown in simulation studies, and an ecology application focusing on modelling bird species occurrence is discussed.
References in corpus (8)
- Bayesian cluster analysis: Point estimation and credible balls
- Discussion on Bayesian Cluster Analysis: Point Estimation and Credible Balls by Sara Wade and Zoubin Ghahramani
- Bayesian Gaussian Copula Factor Models for Mixed Data
- Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models
- A note on the multiplicative gamma process
- Clustering South African households based on their asset status using latent variable models
- A latent factor model for spatial data with informative missingness
- Bayesian time-aligned factor analysis of paired multivariate time series