Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning

8 Jul 2019Ivan GlasserRyan SwekeNicola PancottiJens EisertJ. Ignacio Cirac

Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions... (read more)

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