Post Selection Inference with Kernels
This work addresses the limitation of existing post-selection inference methods that cannot handle non-linearity or structured outputs, offering a more versatile tool for researchers in machine learning and statistics.
The authors tackled the problem of post-selection inference for non-linear and structured data by proposing a kernel-based algorithm, hsicInf, which successfully identified statistically significant features in synthetic experiments and real-world data.
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.