# A block-sparse Tensor Train Format for sample-efficient high-dimensional Polynomial Regression

arXiv: https://arxiv.org/abs/2104.14255 · HTML: https://mlsanity.com/paper/2104.14255/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 29 Apr 2021.

## Builds on (most cited first, 6 of 6)

- [Solving high-dimensional parabolic PDEs using the tensor train format](https://mlsanity.com/paper/2102.11830/) (2021)
- [A least-squares method for sparse low rank approximation of multivariate functions](https://mlsanity.com/paper/1305.0030/) (2013)
- [Tensor-based algorithms for image classification](https://mlsanity.com/paper/1910.02150/) (2019)
- [Pricing high-dimensional Bermudan options with hierarchical tensor formats](https://mlsanity.com/paper/2103.01934/) (2021)
- [Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition](https://mlsanity.com/paper/1407.3023/) (2014)
- [Taylor Expansions of the Value Function Associated with a Bilinear Optimal Control Problem](https://mlsanity.com/paper/1706.05341/) (2017)

## Built on by (most cited first, 3 of 3)

- [From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs](https://mlsanity.com/paper/2307.15496/) (2023)
- [Convergence bounds for nonlinear least squares and applications to tensor recovery](https://mlsanity.com/paper/2108.05237/) (2021)
- [(MPO)2: Multivariate Polynomial Optimization based on Matrix Product Operators](https://mlsanity.com/paper/2607.15916/) (2026)

## Abstract (arXiv)

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.