Bayesian Tensor Network and Optimization Algorithm for Probabilistic Machine Learning
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Describing or calculating the conditional probabilities of multiple events is exponentially expensive. In this work, a natural generalization of Bayesian belief network is proposed by incorporating with tensor network, which is dubbed as Bayesian tensor network (BTN), to efficiently describe the conditional probabilities among multiple sets of events. The complexity of BTN that gives the conditional probabilities of M sets of events scales only polynomially with M. To testify its validity, BTN is implemented to capture the conditional probabilities between images and their classifications, where each feature is mapped to a probability distribution of a set of mutually exclusive events. A rotation optimization method is suggested to update BTN, which avoids gradient vanishing problem and exhibits high efficiency. With a simple tree network structures, BTN exhibits competitive performances on fashion-MNIST dataset. Analogous to the tensor network simulations of quantum systems, the validity of BTN implies an "area law" of fluctuations in image recognition problems.
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