# A least-squares method for sparse low rank approximation of multivariate functions

arXiv: https://arxiv.org/abs/1305.0030 · HTML: https://mlsanity.com/paper/1305.0030/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2013.

## Built on by (most cited first, 10 of 10)

- [A block-sparse Tensor Train Format for sample-efficient high-dimensional Polynomial Regression](https://mlsanity.com/paper/2104.14255/) (2021)
- [Efficient Multidimensional Functional Data Analysis Using Marginal Product Basis Systems](https://mlsanity.com/paper/2107.14728/) (2021)
- [Convergence bounds for nonlinear least squares and applications to tensor recovery](https://mlsanity.com/paper/2108.05237/) (2021)
- [High-Dimensional Uncertainty Quantification via Tensor Regression with Rank Determination and Adaptive Sampling](https://mlsanity.com/paper/2103.17236/) (2021)
- [Uncertainty-aware multi-fidelity surrogate modeling with noisy data](https://mlsanity.com/paper/2401.06447/) (2024)
- [Tensor Decomposition with Unaligned Observations](https://mlsanity.com/paper/2410.14046/) (2024)
- [Surrogate modeling for uncertainty quantification in nonlinear dynamics](https://mlsanity.com/paper/2507.12358/) (2025)
- [Bayesian Kernelized Tensor Factorization as Surrogate for Bayesian Optimization](https://mlsanity.com/paper/2302.14510/) (2023)
- [UQ of 2D Slab Burner DNS: Surrogates, Uncertainty Propagation, and Parameter Calibration](https://mlsanity.com/paper/2411.16693/) (2024)
- [Beyond Additive Decompositions: Interpretability Through Separability](https://mlsanity.com/paper/2605.31200/) (2026)

## Abstract (arXiv)

In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sparsity of low-rank approximations. Sparse low-rank approximations are constructed with a robust updated greedy algorithm which includes an optimal selection of regularization parameters and approximation ranks using cross validation techniques. Numerical examples demonstrate the capability of approximating functions of many variables even when very few function evaluations are available, thus proving the interest of the proposed algorithm for the propagation of uncertainties through complex computational models.