# Decoupling Shrinkage and Selection in Gaussian Linear Factor Analysis

arXiv: https://arxiv.org/abs/2006.11908 · HTML: https://mlsanity.com/paper/2006.11908/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [Heterogeneous Treatment Effect Estimation under Noncompliance in the Illinois Workplace Wellness Study with Bayesian Tree Ensembles](https://mlsanity.com/paper/2408.07765/) (2024)

## Abstract (arXiv)

Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a decision-theoretic approach that brings to light the relation between a sparse representation of the loadings and factor dimension. This relation is done through a summary from information contained in the multivariate posterior. To construct such summary, we introduce a three-step approach. In the first step, the model is fitted with a conservative factor dimension. In the second step, a series of sparse point-estimates, with a decreasing number of factors, is obtained by minimizing an expected predictive loss function. In step three, the degradation in utility in relation to the sparse loadings and factor dimensions is displayed in the posterior summary. The findings are illustrated with applications in classical data from the Factor Analysis literature. We used different prior choices and factor dimensions to demonstrate the flexibility of the proposed method.