Post-selection inference with HSIC-Lasso

Tobias Freidling, Benjamin Poignard, Héctor Climente-González, Makoto Yamada
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:3439-3448, 2021.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Post-selection inference with HSIC-Lasso %A Tobias Freidling %A Benjamin Poignard %A Héctor Climente-González %A Makoto Yamada %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-freidling21a %I PMLR %P 3439--3448 %U https://proceedings.mlr.press/v139/freidling21a.html %V 139 %X 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.
APA
Freidling, T., Poignard, B., Climente-González, H. & Yamada, M.. (2021). Post-selection inference with HSIC-Lasso. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:3439-3448 Available from https://proceedings.mlr.press/v139/freidling21a.html.

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