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

TL;DR

This paper introduces an efficient and powerful selective inference method for Sparse High-order Interaction Models, addressing high dimensionality and selection bias to improve interpretability and reliability in high-stake decision-making.

Contribution

It extends parametric programming for selective inference to high-order interactions and introduces a pruning strategy for computational efficiency.

Findings

Demonstrates improved statistical power on synthetic data.

Shows computational efficiency with real data.

Addresses selection bias in high-dimensional interaction models.

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.