# Efficient MCMC Sampling for Bayesian Matrix Factorization by Breaking Posterior Symmetries

arXiv: https://arxiv.org/abs/2006.04295 · HTML: https://mlsanity.com/paper/2006.04295/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

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

- [Low-rank Bayesian matrix completion via geodesic Hamiltonian Monte Carlo on Stiefel manifolds](https://mlsanity.com/paper/2410.20318/) (2024)

## Abstract (arXiv)

Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to create a conjugate system. This choice of prior leads to simple implementations; however it also causes symmetries in the posterior distribution that can severely reduce the efficiency of Markov-chain Monte-Carlo (MCMC) sampling approaches. In this paper, we propose a simple modification to the prior choice that provably breaks these symmetries and maintains/improves accuracy. Specifically, we provide conditions that the Gaussian prior mean and covariance must satisfy so the posterior does not exhibit invariances that yield sampling difficulties. For example, we show that using non-zero linearly independent prior means significantly lowers the autocorrelation of MCMC samples, and can also lead to lower reconstruction errors.