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

Frontiers in Applied Mathematics and Statistics

关键词: sample efficiency;    homogeneous polynomials;    sparse tensor networks;    alternating least square;    empirical L2 approximation;   

DOI  :  10.3389/fams.2021.702486

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown