Probabilistic tensor analysis with Akaike and Bayesian information criteria

From data mining to computer vision, from visual surveillance to biometrics research, from biomedical imaging to bioinformatics, and from multimedia retrieval to information management, a large amount of data are naturally represented by multidimensional arrays, i.e., tensors. However, conventional probabilistic graphical models with probabilistic inference only model data in vector format, although they are very important in many statistical problems, e.g., model selection. Is it possible to construct multilinear probabilistic graphical models for tensor format data to conduct probabilistic inference, e.g., model selection? This paper provides a positive answer based on the proposed decoupled probabilistic model by developing the probabilistic tensor analysis (PTA), which selects suitable model for tensor format data modeling based on Akaike information criterion (AIC) and Bayesian information criterion (BIC). Empirical studies demonstrate that PTA associated with AIC and BIC selects correct number of models.