Survey on Probabilistic Models of Low-Rank Matrix Factorizations
Tensor factorization methods provide a useful way to extract latent factors from complex multirelational data, and also for predicting missing data. Developing tensor factorization methods for massive tensors, especially when the data are binaryor count-valued (which is true of most real-world tensors), however, remains a challenge. We develop a scalable probabilistic tensor factorization framework that enables us to perform efficient factorization of massive binary and count tensor data. The framework is based on (i) the Pólya-Gamma augmentation strategy which makes the model fully locally conjugate and allows closed-form parameter updates when data are binaryor count-valued; and (ii) an efficient online Expectation Maximization algorithm, which allows processing data in small mini-batches, and facilitates handling massive tensor data. Moreover, various types of constraints on the factor matrices (e.g., sparsity, non-negativity) can be incorporated under the proposed framework, providing good interpretability, which can be useful for qualitative analyses of the results. We apply the proposed framework on analyzing several binaryand count-valued real-world data sets.