A Block-Sparse Tensor Train Format for Sample-Efficient High-Dimensional Polynomial Regression

Low-rank tensors are an established framework for the parametrization of multivariate polynomials. We propose to extend this by including concept block-sparsity efficiently parametrize homogeneous, polynomials with low-rank tensors. This provides a representation general as sum polynomials, represented block-sparse, show that can be concisely single tensor. further prove cases, where particularly well suited showing banded symmetric homogeneous block sizes in block-sparse polynomial space bounded independent number variables. showcase format applying it high-dimensional least squares regression problems demonstrates improved computational resource utilization and sample efficiency.