Generative Modeling via Tree Tensor Network States
This work addresses density estimation for machine learning applications, presenting an incremental improvement by extending tensor-network methods to handle graphical models with loops.
The paper tackles density estimation by introducing a generative modeling framework using tree tensor-network states, achieving sample complexity guarantees validated through numerical experiments.
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.