# Learning Fast Approximations of Sparse Nonlinear Regression

arXiv: https://arxiv.org/abs/2010.13490 · HTML: https://mlsanity.com/paper/2010.13490/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [Deep Learning Techniques for Compressive Sensing-Based Reconstruction and Inference -- A Ubiquitous Systems Perspective](https://mlsanity.com/paper/2105.13191/) (2021)

## Abstract (arXiv)

The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for sparse nonlinear regression problems, a similar idea is rarely exploited due to the complexity of nonlinearity. In this work, we bridge this gap by introducing the Nonlinear Learned Iterative Shrinkage Thresholding Algorithm (NLISTA), which can attain a linear convergence under suitable conditions. Experiments on synthetic data corroborate our theoretical results and show our method outperforms state-of-the-art methods.