Bayesian Robust Tensor Factorization for Incomplete Multiway Data

摘要

We propose a generative model for robust tensor factorization in the presenceof both missing data and outliers. The objective is to explicitly infer theunderlying low-CP-rank tensor capturing the global information and a sparsetensor capturing the local information (also considered as outliers), thusproviding the robust predictive distribution over missing entries. Thelow-CP-rank tensor is modeled by multilinear interactions between multiplelatent factors on which the column sparsity is enforced by a hierarchicalprior, while the sparse tensor is modeled by a hierarchical view of Student-$t$distribution that associates an individual hyperparameter with each elementindependently. For model learning, we develop an efficient closed-formvariational inference under a fully Bayesian treatment, which can effectivelyprevent the overfitting problem and scales linearly with data size. In contrastto existing related works, our method can perform model selection automaticallyand implicitly without need of tuning parameters. More specifically, it candiscover the groundtruth of CP rank and automatically adapt the sparsityinducing priors to various types of outliers. In addition, the tradeoff betweenthe low-rank approximation and the sparse representation can be optimized inthe sense of maximum model evidence. The extensive experiments and comparisonswith many state-of-the-art algorithms on both synthetic and real-world datasetsdemonstrate the superiorities of our method from several perspectives.