# Sparse Recovery With Non-Linear Fourier Features

arXiv: https://arxiv.org/abs/2002.04985 · HTML: https://mlsanity.com/paper/2002.04985/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2020.

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

- [SHRIMP: Sparser Random Feature Models via Iterative Magnitude Pruning](https://mlsanity.com/paper/2112.04002/) (2021)
- [Concentration of Random Feature Matrices in High-Dimensions](https://mlsanity.com/paper/2204.06935/) (2022)
- [A Generalized Weighted Optimization Method for Computational Learning and Inversion](https://mlsanity.com/paper/2201.09223/) (2022)

## Abstract (arXiv)

Random non-linear Fourier features have recently shown remarkable performance in a wide-range of regression and classification applications. Motivated by this success, this article focuses on a sparse non-linear Fourier feature (NFF) model. We provide a characterization of the sufficient number of data points that guarantee perfect recovery of the unknown parameters with high-probability. In particular, we show how the sufficient number of data points depends on the kernel matrix associated with the probability distribution function of the input data. We compare our results with the recoverability bounds for the bounded orthonormal systems and provide examples that illustrate sparse recovery under the NFF model.