# On the Limitation of Kernel Dependence Maximization for Feature Selection

arXiv: https://arxiv.org/abs/2406.06903 · HTML: https://mlsanity.com/paper/2406.06903/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 4 of 4)

- [Kernel Feature Selection via Conditional Covariance Minimization](https://mlsanity.com/paper/1707.01164/) (2017)
- [Variable Selection for Kernel Two-Sample Tests](https://mlsanity.com/paper/2302.07415/) (2023)
- [Variable Selection in Maximum Mean Discrepancy for Interpretable Distribution Comparison](https://mlsanity.com/paper/2311.01537/) (2023)
- [A Theory of Feature Learning in Kernel Models](https://mlsanity.com/paper/2310.11736/) (2023)

## Abstract (arXiv)

A simple and intuitive method for feature selection consists of choosing the feature subset that maximizes a nonparametric measure of dependence between the response and the features. A popular proposal from the literature uses the Hilbert-Schmidt Independence Criterion (HSIC) as the nonparametric dependence measure. The rationale behind this approach to feature selection is that important features will exhibit a high dependence with the response and their inclusion in the set of selected features will increase the HSIC. Through counterexamples, we demonstrate that this rationale is flawed and that feature selection via HSIC maximization can miss critical features.