# More Powerful Selective Kernel Tests for Feature Selection

arXiv: https://arxiv.org/abs/1910.06134 · HTML: https://mlsanity.com/paper/1910.06134/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2019.

## Built on by (most cited first, 6 of 6)

- [MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting](https://mlsanity.com/paper/2306.08777/) (2023)
- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [Variable Selection in Maximum Mean Discrepancy for Interpretable Distribution Comparison](https://mlsanity.com/paper/2311.01537/) (2023)
- [Kernel Biclustering algorithm in Hilbert Spaces](https://mlsanity.com/paper/2208.03675/) (2022)
- [Variable Selection for Comparing High-dimensional Time-Series Data](https://mlsanity.com/paper/2412.06870/) (2024)

## Abstract (arXiv)

Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning on the selection procedure to account for how we have used the data to generate our hypotheses, and prevent information to be used again after selection. Many selective inference (a.k.a. post-selection inference) algorithms typically take this approach but will "over-condition" for sake of tractability. While this practice yields well calibrated statistic tests with controlled false positive rates (FPR), it can incur a major loss in power. In our work, we extend two recent proposals for selecting features using the Maximum Mean Discrepancy and Hilbert Schmidt Independence Criterion to condition on the minimal conditioning event. We show how recent advances in multiscale bootstrap makes conditioning on the minimal selection event possible and demonstrate our proposal over a range of synthetic and real world experiments. Our results show that our proposed test is indeed more powerful in most scenarios.