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Matrix factorization (MF) has been widely applied to collaborative filteringin recommendation systems. Its Bayesian variants can derive posteriordistributions of user and item embeddings, and are more robust to sparseratings. However, the Bayesian methods are restricted by their update rules forthe posterior parameters due to the conjugacy of the priors and the likelihood.Variational autoencoders (VAE) can address this issue by capturing complexmappings between the posterior parameters and the data. However, currentresearch on VAEs for collaborative filtering only considers the mappings basedon the explicit data information while the implicit embedding information isoverlooked. In this paper, we first derive evidence lower bounds (ELBO) forBayesian MF models from two viewpoints: user-oriented and item-oriented. Basedon the ELBOs, we propose a VAE-based Bayesian MF framework. It leverages notonly the data but also the embedding information to approximate the user-itemjoint distribution. As suggested by the ELBOs, the approximation is iterativewith cross feedback of user and item embeddings into each other's encoders.More specifically, user embeddings sampled at the previous iteration are fed tothe item-side encoders to estimate the posterior parameters for the itemembeddings at the current iteration, and vice versa. The estimation alsoattends to the cross-fed embeddings to further exploit useful information. Thedecoder then reconstructs the data via the matrix factorization over thecurrently re-sampled user and item embeddings.

Leveraging Cross Feedback of User and Item Embeddings with Attention for Variational Autoencoder based Collaborative Filtering