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

Ruixuan Xu, Xiangxiang Weng
6/11/2025
cs.LGstat.ML

No official code found. Best implementation: xx-Weng/Comparing-MCMC-and-VI-for-Bayesian-Probabilistic-Matrix-Factorization-on-the-MovieLens-Dataset (1 star, last commit 2025-06-12).

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.

View on arXivView PDF

Code Implementations(1)

xx-Weng/Comparing-MCMC-and-VI-for-Bayesian-Probabilistic-Matrix-Factorization-on-the-MovieLens-DatasetCommunity66%

This is the code source for the course report https://www.arxiv.org/abs/2506.09928

10PythonJun 12, 20251 years ago

Similar Papers

Bayesian neural networks via MCMC: a Python-based tutorial

80% match1 repo752023

MCMC-driven learning

77% match2024

MFAI: A Scalable Bayesian Matrix Factorization Approach to Leveraging Auxiliary Information

77% match1 repo92023

Bayesian Estimation and Tuning-Free Rank Detection for Probability Mass Function Tensors

76% match2024

Bayesian Parametric Matrix Models: Principled Uncertainty Quantification for Spectral Learning

76% match2025

Machine Learning and the Future of Bayesian Computation

76% match2023

Cite this paper

@article{xu2025course,
  title  = {Course Project Report: Comparing MCMC and Variational Inference for Bayesian Probabilistic Matrix Factorization on the MovieLens Dataset},
  author = {Ruixuan Xu and Xiangxiang Weng},
  year   = {2025},
  eprint = {2506.09928},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2506.09928v2}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2506.09928.svg)](https://codeofpaper.com/paper/2506.09928)

Discussion