# Course Project Report: Comparing MCMC and Variational Inference for Bayesian Probabilistic Matrix Factorization on the MovieLens Dataset

arXiv: https://arxiv.org/abs/2506.09928 · HTML: https://mlsanity.com/paper/2506.09928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 10 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 1 of 1)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)

## Abstract (arXiv)

This is a course project report with complete methodology, experiments, references and mathematical derivations. Matrix factorization [1] is a widely used technique in recommendation systems. Probabilistic Matrix Factorization (PMF) [2] extends traditional matrix factorization by incorporating probability distributions over latent factors, allowing for uncertainty quantification. However, computing the posterior distribution is intractable due to the high-dimensional integral. To address this, we employ two Bayesian inference methods: Markov Chain Monte Carlo (MCMC) [3, 4] and Variational Inference (VI) [5, 6] to approximate the posterior. We evaluate their performance on MovieLens dataset [7] and compare their convergence speed, predictive accuracy, and computational efficiency. Experimental results demonstrate that VI offers faster convergence, while MCMC provides more accurate posterior estimates.