# On the identifiability of Bayesian factor analytic models

arXiv: https://arxiv.org/abs/2004.05105 · HTML: https://mlsanity.com/paper/2004.05105/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2020.

## Built on by (most cited first, 5 of 5)

- [Bayesian Joint Additive Factor Models for Multiview Learning](https://mlsanity.com/paper/2406.00778/) (2024)
- [Discovering Hierarchical Latent Capabilities of Language Models via Causal Representation Learning](https://mlsanity.com/paper/2506.10378/) (2025)
- [Linear-cost unbiased posterior estimates for crossed effects and matrix factorization models via couplings](https://mlsanity.com/paper/2410.08939/) (2024)
- [Factorized Fusion Shrinkage for Dynamic Relational Data](https://mlsanity.com/paper/2210.00091/) (2022)
- [A Bayesian sparse factor model with adaptive posterior concentration](https://mlsanity.com/paper/2305.18488/) (2023)

## Abstract (arXiv)

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to generate samples from the posterior distribution. We introduce a post-processing scheme in order to deal with rotation, sign and permutation invariance of the MCMC sample. The exact version of the contributed algorithm requires to solve 2q assignment problems per (retained) MCMC iteration, where q denotes the number of factors of the fitted model. For large numbers of factors two approximate schemes based on simulated annealing are also discussed. We demonstrate that the proposed method leads to interpretable posterior distributions using synthetic and publicly available data from typical factor analytic models as well as mixtures of factor analyzers. An R package is available online at CRAN web-page.