Generative Modeling via Hierarchical Tensor Sketching
This addresses density estimation in high-dimensional spaces, likely for machine learning applications, but appears incremental as it builds on existing tensor-network and SVD techniques.
The paper tackles approximating high-dimensional probability densities via empirical distributions using a hierarchical tensor-network approach, achieving linear complexity scaling in dimension and demonstrating effectiveness through numerical experiments.
We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear equations for tensor cores in this tensor network. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density. An analysis of estimation error demonstrates the effectiveness of this method through several numerical experiments.