A block-sparse Tensor Train Format for sample-efficient high-dimensional Polynomial Regression
This is an incremental improvement for researchers in high-dimensional data analysis and tensor methods.
The paper tackled high-dimensional polynomial regression by proposing a block-sparse tensor train format to improve sample efficiency, and numerical experiments showed enhanced computational resource utilization.
Low-rank tensors are an established framework for high-dimensional least-squares problems. We propose to extend this framework by including the concept of block-sparsity. In the context of polynomial regression each sparsity pattern corresponds to some subspace of homogeneous multivariate polynomials. This allows us to adapt the ansatz space to align better with known sample complexity results. The resulting method is tested in numerical experiments and demonstrates improved computational resource utilization and sample efficiency.