Generative Modeling via Tree Tensor Network States

TL;DR

This paper introduces a novel density estimation framework using tree tensor-network states, employing Chow-Liu algorithms and sketching techniques to handle graphical models with loops, supported by theoretical guarantees and numerical validation.

Contribution

It develops a new tensor-network based density estimation method with innovative sketching functions for loopy graphical models, including theoretical analysis and practical experiments.

Findings

Sample complexity guarantees established

Effective handling of loopy graphical models

Numerical experiments validate the approach

Abstract

In this paper, we present a density estimation framework based on tree tensor-network states. The proposed method consists of determining the tree topology with Chow-Liu algorithm, and obtaining a linear system of equations that defines the tensor-network components via sketching techniques. Novel choices of sketch functions are developed in order to consider graphical models that contain loops. Sample complexity guarantees are provided and further corroborated by numerical experiments.