Selective Inference for High-order Interaction Features Selected in a Stepwise Manner

In this paper, we study a stepwise feature selection algorithm for a high-order interaction model and we propose a new statistical inference for selected high-order interaction features. Feature selection and statistical inference for high-order interaction features are challenging tasks because the possible number of those interactions is extremely large. Our main contribution is to extend recently developed selective inference framework to high-order interaction model by developing a pruning technique for searching over tree which represents high-order interaction features. We demonstrate the effectiveness of the proposed approach by applying it to several synthetic problems and an HIV drug resistance prediction problem.