Post-selection inference with HSIC-Lasso

• URL: http://arxiv.org/abs/2010.15659v2
• Date: Thu, 17 Jun 2021 11:19:29 GMT
• Title: Post-selection inference with HSIC-Lasso
• Authors: Tobias Freidling, Benjamin Poignard, H\'ector Climente-Gonz\'alez, Makoto Yamada
• Abstract summary: We propose a selective inference procedure using 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.
• Score: 19.928884107444908
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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