Course Project Report: Comparing MCMC and Variational Inference for Bayesian Probabilistic Matrix Factorization on the MovieLens Dataset
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918057290498048 |
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| author | Xu, Ruixuan Weng, Xiangxiang |
| author_facet | Xu, Ruixuan Weng, Xiangxiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Course Project Report: Comparing MCMC and Variational Inference for Bayesian Probabilistic Matrix Factorization on the MovieLens Dataset Xu, Ruixuan Weng, Xiangxiang Machine Learning 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. |
| title | Course Project Report: Comparing MCMC and Variational Inference for Bayesian Probabilistic Matrix Factorization on the MovieLens Dataset |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.09928 |