Post Selection Inference with Kernels
Makoto Yamada, Yuta Umezu, Kenji Fukumizu, Ichiro Takeuchi
Abstract
Finding a set of statistically significant features from complex data (e.g., nonlinear and/or multi-dimensional output data) is important for scientific discovery and has a number of practical applications including biomarker discovery. In this paper, we propose a kernel-based post-selection inference (PSI) algorithm that can find a set of statistically significant features from non-linearly related data. Specifically, our PSI algorithm is based on independence measures, and we call it the Hilbert-Schmidt Independence Criterion (HSIC)-based PSI algorithm (hsicInf). The novelty of hsicInf is that it can handle non-linearity and/or multi-variate/multi-class outputs through kernels. Through synthetic experiments, we show that hsicInf can find a set of statistically significant features for both regression and classification problems. We applied hsicInf to real-world datasets and show that it can successfully identify important features.
BibTeX
@InProceedings{pmlr-v84-yamada18a,
title = {Post Selection Inference with Kernels},
author = {Yamada, Makoto and Umezu, Yuta and Fukumizu, Kenji and Takeuchi, Ichiro},
booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics},
pages = {152--160},
year = {2018},
editor = {Storkey, Amos and Perez-Cruz, Fernando},
volume = {84},
series = {Proceedings of Machine Learning Research},
month = {09--11 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v84/yamada18a/yamada18a.pdf},
url = {https://proceedings.mlr.press/v84/yamada18a.html},
abstract = {Finding a set of statistically significant features from complex data (e.g., nonlinear and/or multi-dimensional output data) is important for scientific discovery and has a number of practical applications including biomarker discovery. In this paper, we propose a kernel-based post-selection inference (PSI) algorithm that can find a set of statistically significant features from non-linearly related data. Specifically, our PSI algorithm is based on independence measures, and we call it the Hilbert-Schmidt Independence Criterion (HSIC)-based PSI algorithm (hsicInf). The novelty of hsicInf is that it can handle non-linearity and/or multi-variate/multi-class outputs through kernels. Through synthetic experiments, we show that hsicInf can find a set of statistically significant features for both regression and classification problems. We applied hsicInf to real-world datasets and show that it can successfully identify important features. }
}