Probabilistic Tensor Analysis with Akaike and Bayesian Information Criteria

Authors:
Dacheng Tao;Jimeng Sun;Xindong Wu;Xuelong Li;Jialie Shen;Stephen J. Maybank;Christos Faloutsos
Affiliations:
Department of Computing, Hong Kong Polytechnic University, Hong Kong;Department of Computer Science, Carnegie Mellon University, Pittsburgh, USA;Department of Computer Science, University of Vermont, Burlington, USA;Sch. Computer Science & Info Systems, Birkbeck, University of London, London, UK;School of Information Systems, Singapore Management University, Singapore;Sch. Computer Science & Info Systems, Birkbeck, University of London, London, UK;Department of Computer Science, Carnegie Mellon University, Pittsburgh, USA
Venue:
Neural Information Processing
Year:
2007

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Abstract

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 vectorformat, although they are very important in many statistical problems, e.g., model selection. Is it possible to construct multilinear probabilistic graphical models for tensorformat 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 tensorformat 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.