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Beyond their origin in modeling many-body quantum systems, tensor networkshave emerged as a promising class of models for solving machine learningproblems, notably in unsupervised generative learning. While possessing manydesirable features arising from their quantum-inspired nature, tensor networkgenerative models have previously been largely restricted to binary orcategorical data, limiting their utility in real-world modeling problems. Weovercome this by introducing a new family of tensor network generative modelsfor continuous data, which are capable of learning from distributionscontaining continuous random variables. We develop our method in the setting ofmatrix product states, first deriving a universal expressivity theorem provingthe ability of this model family to approximate any reasonably smoothprobability density function with arbitrary precision. We then benchmark theperformance of this model on several synthetic and real-world datasets, findingthat the model learns and generalizes well on distributions of continuous anddiscrete variables. We develop methods for modeling different data domains, andintroduce a trainable compression layer which is found to increase modelperformance given limited memory or computational resources. Overall, ourmethods give important theoretical and empirical evidence of the efficacy ofquantum-inspired methods for the rapidly growing field of generative learning.

Generative Learning of Continuous Data by Tensor Networks