Post Selection Inference with Kernels

TL;DR

This paper introduces a kernel-based post selection inference algorithm, hsicInf, capable of handling non-linear and structured data, enabling feature significance testing in complex regression and classification tasks.

Contribution

It presents a novel PSI algorithm using HSIC kernels that extends applicability to non-linear and structured data, unlike previous methods.

Findings

Successfully identifies significant features in synthetic data

Effectively detects important features in real-world data

Handles multi-dimensional and multi-label outputs

Abstract

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.