Selective Inference for Sparse High-Order Interaction Models
Shinya Suzumura, Kazuya Nakagawa, Yuta Umezu, Koji Tsuda, Ichiro Takeuchi
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.
BibTeX
@InProceedings{pmlr-v70-suzumura17a,
title = {Selective Inference for Sparse High-Order Interaction Models},
author = {Shinya Suzumura and Kazuya Nakagawa and Yuta Umezu and Koji Tsuda and Ichiro Takeuchi},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {3338--3347},
year = {2017},
editor = {Precup, Doina and Teh, Yee Whye},
volume = {70},
series = {Proceedings of Machine Learning Research},
month = {06--11 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v70/suzumura17a/suzumura17a.pdf},
url = {https://proceedings.mlr.press/v70/suzumura17a.html},
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.}
}