# Large-scale Nonlinear Variable Selection via Kernel Random Features

arXiv: https://arxiv.org/abs/1804.07169 · HTML: https://mlsanity.com/paper/1804.07169/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2018.

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

- [Scalable Randomized Kernel Methods for Multiview Data Integration and Prediction](https://mlsanity.com/paper/2304.04692/) (2023)
- [On the Complexity-Faithfulness Trade-off of Gradient-Based Explanations](https://mlsanity.com/paper/2508.10490/) (2025)
- [RFFNet: Large-Scale Interpretable Kernel Methods via Random Fourier Features](https://mlsanity.com/paper/2211.06410/) (2022)

## Abstract (arXiv)

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sidesteps the typical poor scaling properties of kernel methods by mapping the inputs into a relatively low-dimensional space of random features. The algorithm discovers the variables relevant for the regression task together with learning the prediction model through learning the appropriate nonlinear random feature maps. We demonstrate the outstanding performance of our method on a set of large-scale synthetic and real datasets.