# Post Selection Inference with Kernels

arXiv: https://arxiv.org/abs/1610.03725 · HTML: https://mlsanity.com/paper/1610.03725/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2016.

## Built on by (most cited first, 13 of 13)

- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation](https://mlsanity.com/paper/2104.10840/) (2021)
- [Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference](https://mlsanity.com/paper/2110.08989/) (2021)
- [CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference](https://mlsanity.com/paper/2310.14608/) (2023)
- [Selective Inference for Changepoint detection by Recurrent Neural Network](https://mlsanity.com/paper/2311.14964/) (2023)
- [LoRASuite: Efficient LoRA Adaptation Across Large Language Model Upgrades](https://mlsanity.com/paper/2505.13515/) (2025)
- [Statistical Test for Auto Feature Engineering by Selective Inference](https://mlsanity.com/paper/2410.19768/) (2024)
- [Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptation](https://mlsanity.com/paper/2508.07049/) (2025)
- [Bounded P-values in Parametric Programming-based Selective Inference](https://mlsanity.com/paper/2307.11351/) (2023)
- [Few-shot Learning for Unsupervised Feature Selection](https://mlsanity.com/paper/2107.00816/) (2021)
- [Neural Networks beyond explainability: Selective inference for sequence motifs](https://mlsanity.com/paper/2212.12542/) (2022)
- [Statistical Inference for Clustering-based Anomaly Detection](https://mlsanity.com/paper/2504.18633/) (2025)
- [Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathology](https://mlsanity.com/paper/2609.31712/) (2026)

## Abstract (arXiv)

We propose a novel kernel based post selection inference (PSI) algorithm, which can not only handle non-linearity in data but also structured output such as multi-dimensional and multi-label outputs. Specifically, we develop a PSI algorithm for independence measures, and propose the Hilbert-Schmidt Independence Criterion (HSIC) based PSI algorithm (hsicInf). The novelty of the proposed algorithm is that it can handle non-linearity and/or structured data through kernels. Namely, the proposed algorithm can be used for wider range of applications including nonlinear multi-class classification and multi-variate regressions, while existing PSI algorithms cannot handle them. Through synthetic experiments, we show that the proposed approach can find a set of statistically significant features for both regression and classification problems. Moreover, we apply the hsicInf algorithm to a real-world data, and show that hsicInf can successfully identify important features.