Tensor tree learns hidden relational structures in data to construct generative models

Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the quantum wave function amplitude represented by a tensor tree. The key idea is dynamically optimizing the tree structure that minimizes the bond mutual information. The proposed method offers enhanced performance and uncovers hidden relational structures in the target data. We illustrate potential practical applications with four examples: (i) random patterns, (ii) QMNIST hand-written digits, (iii) Bayesian networks, and (iv) the stock price fluctuation pattern in S&P500. In (i) and (ii), strongly correlated variables were concentrated near the center of the network; in (iii), the causality pattern was identified; and, in (iv), a structure corresponding to the eleven sectors emerged.