Post-selection inference with HSIC-Lasso
Tobias Freidling, Benjamin Poignard, Héctor Climente-González, Makoto Yamada
Abstract
Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection inference. Indeed, the selected features can be significantly flawed when the selection procedure is not accounted for. We propose a selective inference procedure using the so-called model-free "HSIC-Lasso" based on the framework of truncated Gaussians combined with the polyhedral lemma. We then develop an algorithm, which allows for low computational costs and provides a selection of the regularisation parameter. The performance of our method is illustrated by both artificial and real-world data based experiments, which emphasise a tight control of the type-I error, even for small sample sizes.
BibTeX
@InProceedings{pmlr-v139-freidling21a,
title = {Post-selection inference with HSIC-Lasso},
author = {Freidling, Tobias and Poignard, Benjamin and Climente-Gonz{\'a}lez, H{\'e}ctor and Yamada, Makoto},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {3439--3448},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/freidling21a/freidling21a.pdf},
url = {https://proceedings.mlr.press/v139/freidling21a.html},
abstract = {Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection inference. Indeed, the selected features can be significantly flawed when the selection procedure is not accounted for. We propose a selective inference procedure using the so-called model-free "HSIC-Lasso" based on the framework of truncated Gaussians combined with the polyhedral lemma. We then develop an algorithm, which allows for low computational costs and provides a selection of the regularisation parameter. The performance of our method is illustrated by both artificial and real-world data based experiments, which emphasise a tight control of the type-I error, even for small sample sizes.}
}