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It is known that describing or calculating the conditional probabilities ofmultiple events is exponentially expensive. In this work, Bayesian tensornetwork (BTN) is proposed to efficiently capture the conditional probabilitiesof multiple sets of events with polynomial complexity. BTN is a directedacyclic graphical model that forms a subset of TN. To testify its validity forexponentially many events, BTN is implemented to the image recognition, wherethe classification is mapped to capturing the conditional probabilities in anexponentially large sample space. Competitive performance is achieved by theBTN with simple tree network structures. Analogous to the tensor networksimulations of quantum systems, the validity of the simple-tree BTN implies an``area law'' of fluctuations in image recognition problems.

Bayesian Tensor Network with Polynomial Complexity for Probabilistic Machine Learning