对比两种方法在推荐系统中的后验推断效果。
Course Project Report: Comparing MCMC and Variational Inference for Bayesian Probabilistic Matrix Factorization on the MovieLens Dataset
- 用MCMC和变分推断近似矩阵分解的后验分布。
- 变分推断收敛更快，马尔可夫链蒙特卡洛更准。
- 适合想了解贝叶斯推荐系统推断方法的研究者。
矩阵分解是推荐系统中广泛使用的技术。概率矩阵分解（PMF）通过在隐因子上引入概率分布，实现不确定性量化，但后验分布计算因高维积分而不可行。为此，本文采用马尔可夫链蒙特卡洛（MCMC）和变分推断（VI）两种贝叶斯推断方法近似后验分布，并在MovieLens数据集上评估其性能，比较收敛速度、预测准确性和计算效率。实验结果表明，变分推断收敛更快，而马尔可夫链蒙特卡洛能提供更精确的后验估计。
原文摘要 · Abstract (English)
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.
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