Bayesian Tensor Network with Polynomial Complexity for Probabilistic Machine Learning

Abstract

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

7 pages, 5 figures; in the second version, results of the BTN with a new structure were added; other modifications including the formulation of Bayes' equation in tensor forms were made

References in corpus (5)

• Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
• Tensor renormalization group approach to 2D classical lattice models
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Tree Tensor Networks for Generative Modeling
• The area law and real-space renormalization