  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.
