# Kernel Feature Selection via Conditional Covariance Minimization

arXiv: https://arxiv.org/abs/1707.01164 · HTML: https://mlsanity.com/paper/1707.01164/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2017.

## Built on by (most cited first, 20 of 20)

- [How rotational invariance of common kernels prevents generalization in high dimensions](https://mlsanity.com/paper/2104.04244/) (2021)
- [The Rashomon Importance Distribution: Getting RID of Unstable, Single Model-based Variable Importance](https://mlsanity.com/paper/2309.13775/) (2023)
- [Where to Pay Attention in Sparse Training for Feature Selection?](https://mlsanity.com/paper/2211.14627/) (2022)
- [FedSDG-FS: Efficient and Secure Feature Selection for Vertical Federated Learning](https://mlsanity.com/paper/2302.10417/) (2023)
- [Efficient Decompositional Rule Extraction for Deep Neural Networks](https://mlsanity.com/paper/2111.12628/) (2021)
- [Contextual Feature Selection with Conditional Stochastic Gates](https://mlsanity.com/paper/2312.14254/) (2023)
- [Graph Convolutional Network-based Feature Selection for High-dimensional and Low-sample Size Data](https://mlsanity.com/paper/2211.14144/) (2022)
- [Explainable Machine Learning for Breakdown Prediction in High Gradient RF Cavities](https://mlsanity.com/paper/2202.05610/) (2022)
- [Learning Active Subspaces and Discovering Important Features with Gaussian Radial Basis Functions Neural Networks](https://mlsanity.com/paper/2307.05639/) (2023)
- [On the Complexity-Faithfulness Trade-off of Gradient-Based Explanations](https://mlsanity.com/paper/2508.10490/) (2025)
- [An Embedded Feature Selection Framework for Control](https://mlsanity.com/paper/2206.11064/) (2022)
- [Comprehend, Divide, and Conquer: Feature Subspace Exploration via Multi-Agent Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2504.17356/) (2025)
- [A Compositional Kernel Model for Feature Learning](https://mlsanity.com/paper/2509.14158/) (2025)
- [Experimental Design for Multi-Channel Imaging via Task-Driven Feature Selection](https://mlsanity.com/paper/2210.06891/) (2022)
- [RFFNet: Large-Scale Interpretable Kernel Methods via Random Fourier Features](https://mlsanity.com/paper/2211.06410/) (2022)
- [End-to-end Feature Selection Approach for Learning Skinny Trees](https://mlsanity.com/paper/2310.18542/) (2023)
- [EasyFS: an Efficient Model-free Feature Selection Framework via Elastic Transformation of Features](https://mlsanity.com/paper/2402.05954/) (2024)
- [On the Limitation of Kernel Dependence Maximization for Feature Selection](https://mlsanity.com/paper/2406.06903/) (2024)
- [ICAFS: Inter-Client-Aware Feature Selection for Vertical Federated Learning](https://mlsanity.com/paper/2504.10851/) (2025)
- [Where to Intervene: Action Selection in Deep Reinforcement Learning](https://mlsanity.com/paper/2507.04187/) (2025)

## Abstract (arXiv)

We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to perform feature selection via a constrained optimization problem involving the trace of the conditional covariance operator. We prove various consistency results for this procedure, and also demonstrate that our method compares favorably with other state-of-the-art algorithms on a variety of synthetic and real data sets.