Neural variational matrix factorization for collaborative filtering in recommendation systems

Teng Xiao, Hong Shen

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


Matrix factorization as a popular technique for collaborative filtering in recommendation systems computes the latent factors for users and items by decomposing a user-item rating matrix. Most matrix factorization methods including probabilistic matrix factorization that projects (parameterized) users and items probabilistic matrices to maximize their inner product suffer from data sparsity and result in poor latent representations of users and items. To alleviate these problems, we propose a novel deep generative model, namely Neural Variational Matrix Factorization, that incorporates side information (features) of both users and items to capture better latent representations of them for more effective collaborative-filtering recommendation. Our model consists of two end-to-end variational autoencoder neural networks, namely user neural network and item neural network respectively, that are capable of learning complex nonlinear distributed representations of users and items through our proposed variational inference. We present a Stochastic Gradient Variational Bayes estimator to estimate the intractable posterior distributions of latent factors of users and items and parameters of our model, and derive the variational evidence lower bounds of the model. Experiments conducted on three publicly available datasets show that our model significantly outperforms the state-of-the-art methods on recommendation accuracy measured by Hit Ratio and Normalized Discounted Cumulative Gain respectively.

Original languageEnglish
Pages (from-to)3558-3569
Number of pages12
JournalApplied Intelligence
Issue number10
Publication statusPublished - 1 Oct 2019
Externally publishedYes


  • Collaborative filtering
  • Deep generative process
  • Matrix factorization
  • Recommendation
  • Variational inference


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