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Title: Post-selection Inference with HSIC-Lasso (ICML 2021)
Detecting influential features in non-linear and/or high-dimensional data is an increasingly important task in machine learning. However, inference on the chosen features can be significantly flawed when the selection procedure is not accounted for. We propose a post-selection 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 the proposed method is illustrated by both artificial and real-world data based experiments, which exhibit a tight control of the type-I error, even for small sample sizes.
Tobias Freidling obtained a Bachelor and Master degree in Mathematics from the Ludwig-Maximilian University and Technical University of Munich, respectively. From March to August 2020 he was a research student at Prof. Yamada’s group at Kyoto University and worked on the project presented in this talk. Since October 2020, Tobias is a PhD student at the University of Cambridge, supervised by Qingyuan Zhao. His research focuses on causal inference, sensitivity analysis and selective inference.
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