Course Project Report: Comparing MCMC and Variational Inference for Bayesian Probabilistic Matrix Factorization on the MovieLens Dataset
Abstract
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.
Cite
@article{arxiv.2506.09928,
title = {Course Project Report: Comparing MCMC and Variational Inference for Bayesian Probabilistic Matrix Factorization on the MovieLens Dataset},
author = {Ruixuan Xu and Xiangxiang Weng},
journal= {arXiv preprint arXiv:2506.09928},
year = {2025}
}
Comments
11 pages, 2 figures. This document is a course project report. Some derivations are presented in a simplified form. For more detailed discussions and comprehensive proofs, please refer to the references cited in this report. v2 replacement: we have modified the title to better match our content. We have also updated the references to be more complete, including the link to our code