# Generalized infinite factorization models

arXiv: https://arxiv.org/abs/2103.10333 · HTML: https://mlsanity.com/paper/2103.10333/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2021.

## Built on by (most cited first, 6 of 6)

- [Bayesian Joint Additive Factor Models for Multiview Learning](https://mlsanity.com/paper/2406.00778/) (2024)
- [Choosing the number of factors in factor analysis with incomplete data via a hierarchical Bayesian information criterion](https://mlsanity.com/paper/2204.09086/) (2022)
- [Accelerated structured matrix factorization](https://mlsanity.com/paper/2212.06504/) (2022)
- [Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis](https://mlsanity.com/paper/2303.00473/) (2023)
- [A Bayesian Methodology for Estimation for Sparse Canonical Correlation](https://mlsanity.com/paper/2310.19621/) (2023)
- [An efficient adaptive dimension selection algorithm for multidimensional probit graded response models](https://mlsanity.com/paper/2607.17654/) (2026)

## Abstract (arXiv)

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.