Fast and More Powerful Selective Inference for Sparse High-order Interaction Model

• URL: http://arxiv.org/abs/2106.04929v1
• Date: Wed, 9 Jun 2021 09:22:42 GMT
• Title: Fast and More Powerful Selective Inference for Sparse High-order Interaction Model
• Authors: Diptesh Das, Vo Nguyen Le Duy, Hiroyuki Hanada, Koji Tsuda, Ichiro Takeuchi
• Abstract summary: We consider Sparse High-order Interaction Model (SHIM) in this study. Finding statistically significant high-order interactions is challenging due to intrinsic high dimensionality of the effects. Our main contribution is to extend the recently developed parametric programming approach for selective inference to high-order interaction models.
• Score: 17.549975092550074
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Automated high-stake decision-making such as medical diagnosis requires models with high interpretability and reliability. As one of the interpretable and reliable models with good prediction ability, we consider Sparse High-order Interaction Model (SHIM) in this study. However, finding statistically significant high-order interactions is challenging due to the intrinsic high dimensionality of the combinatorial effects. Another problem in data-driven modeling is the effect of "cherry-picking" a.k.a. selection bias. Our main contribution is to extend the recently developed parametric programming approach for selective inference to high-order interaction models. Exhaustive search over the cherry tree (all possible interactions) can be daunting and impractical even for a small-sized problem. We introduced an efficient pruning strategy and demonstrated the computational efficiency and statistical power of the proposed method using both synthetic and real data.

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