Probabilistic matrix factorization (PMF) is the most popular method among low-rank matrix approximation approaches that address the sparsity problem in collaborative filtering for recommender systems. PMF depends on the classical maximum a posteriori estimator for estimating model parameters; however, these approaches are vulnerable to overfitting because of the nature of a single point estimation that is pursued by these models. An alternative approach to PMF is a Bayesian PMF model that suggests the Markov chain Monte Carlo algorithm as a full estimation for approximate intractable posterior over model parameters. However, despite its success in increasing prediction, it has a high computational cost. To this end, we proposed a novel Bayesian deep learning-based model treatment, namely, variational autoencoder Bayesian matrix factorization (VABMF). The proposed model uses stochastic gradient variational Bayes to estimate intractable posteriors and expectation–maximization-style estimators to learn model parameters. The model was evaluated on the basis of three MovieLens datasets, namely, Ml-100k, Ml-1M, and Ml-10M. Experimental results showed that our proposed VABMF model significantly outperforms state-of-the-art RS.

概率矩阵分解（PMF）是低秩矩阵近似方法中最受欢迎的方法，该方法解决了推荐系统协作过滤中的稀疏性问题。PMF依赖于经典最大值后验估计器来估计模型参数；然而，由于这些模型所追求的单点估计的性质，这些方法很容易过度拟合。PMF的另一种方法是贝叶斯PMF模型，该模型建议将马尔可夫链蒙特卡罗算法作为模型参数的近似难处理后验的完整估计。然而，尽管其成功地增加了预测，但是它具有很高的计算成本。为此，我们提出了一种新颖的基于贝叶斯深度学习的模型处理方法，即 变分自动编码器贝叶斯矩阵分解（VABMF）。所提出的模型使用随机梯度变分贝叶斯估计难处理的后验，并使用期望最大化样式估计器来学习模型参数。基于三个MovieLens数据集，即Ml-100k，Ml-1M和Ml-10M，对模型进行了评估。实验结果表明，我们提出的VABMF模型明显优于最新的RS。