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

TL;DR

This paper introduces a tensor tree-based generative model that dynamically optimizes its structure to uncover hidden relational patterns in diverse data types, enhancing performance and interpretability.

Contribution

It presents a novel tensor tree framework that learns and optimizes relational structures in data for improved generative modeling.

Findings

Identified causality patterns in Bayesian networks.

Discovered sector structures in stock market data.

Concentrated correlated variables in handwritten digit data.

Abstract

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 amplitude of the quantum wave function 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 handwritten digits, (iii) Bayesian networks, and (iv) the pattern of stock price fluctuation pattern in S&P500. In (i) and (ii), the 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.