Selective Inference for Sparse High-Order Interaction Models

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Shinya Suzumura, Kazuya Nakagawa, Yuta Umezu, Koji Tsuda, Ichiro Takeuchi ;
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3338-3347, 2017.

Abstract

Finding statistically significant high-order interactions in predictive modeling is important but challenging task because the possible number of high-order interactions is extremely large (e.g., $> 10^{17}$). In this paper we study feature selection and statistical inference for sparse high-order interaction models. Our main contribution is to extend recently developed selective inference framework for linear models to high-order interaction models by developing a novel algorithm for efficiently characterizing the selection event for the selective inference of high-order interactions. We demonstrate the effectiveness of the proposed algorithm by applying it to an HIV drug response prediction problem.

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