We consider the probabilistic analogue to neural network matrix factorization (Dziugaite & Roy, 2015), which we construct with Bayesian neural networks and fit with variational inference. We find that a linear model fit with variational inference can attain equivalent predictive performance to the neural network variants on the Movielens data sets. We discuss the implications of this result, which include some suggestions on the pros and cons of using the neural network construction, as well as the variational approach to inference. A probabilistic approach is required in some cases, however, such as when considering the important class of stochastic blockmodels. We describe a variational inference algorithm for a neural network matrix factorization model with nonparametric block structure and evaluate it on the NIPS co-authorship data set.

使用贝叶斯神经网络和变分推断构建的概率神经网络矩阵因子分解模型能够获得与常规神经网络变体相当的预测性能，这一概率方法在处理随机块模型时非常重要，同时还提出了一个非参数块结构的神经网络矩阵分解模型的变分推断算法，并在 NIPS 合著数据集上评估了其性能。

神经网络矩阵分解的变分推断及其在随机块模型中的应用