Statistically Robust Sparse High-order Interaction Model

Abstract Deep learning models often achieve high accuracy but lack interpretability, making them unsuitable for critical applications such as medical diagnosis, biomolecule design, criminal justice, etc. The Sparse High-order Interaction Model (SHIM) addresses this limitation by providing both transparency and predictive reliability. However, real-world data often contain outliers, which can distort model performance. To overcome this, we propose Huberized-SHIM, an extension of SHIM that integrates Huber loss-based robust regression to mitigate the impact of outliers. We introduce a homotopy-based exact regularization path algorithm and a novel tree-pruning criterion to efficiently manage interaction complexity. Additionally, we incorporate the conformal prediction framework to enhance statistical reliability. Empirical evaluations on synthetic and real-world datasets demonstrate the superior robustness and accuracy of Huberized-SHIM in high-stakes decision-making contexts.