Generative modeling via tree tensor network states

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 the 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. For a wide class of d-dimensional density functions admitting the proposed ansatz, fast $$O(d)$$ sample complexity guarantees are provided and further corroborated by numerical experiments.