Reluctant Interaction Inference after Additive Modeling

2025-06-02

AI Summary

A fundamental modeling decision—whether to augment a fitted additive model with interaction terms—lacks a statistically rigorous framework for hypothesis testing. Method: We propose the first selective inference–based statistical test for this problem, using the sparse additive model (SPAM) as the null hypothesis. We formalize the “interaction hesitation” principle as a data-adaptive selective hypothesis test and introduce external randomization to correct overfitting bias, enabling rigorous construction of conditional p-values that provably control Type I error. Contribution/Results: Our method is validated on synthetic and real-world datasets: with minimal randomization, it significantly outperforms naive tests and data-splitting approaches—achieving strict false rejection rate control while markedly improving statistical power. This work establishes a new paradigm for interaction assessment in interpretable modeling: statistically valid, computationally feasible, and grounded in selective inference theory.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Additive models enjoy the flexibility of nonlinear models while still being readily understandable to humans. By contrast, other nonlinear models, which involve interactions between features, are not only harder to fit but also substantially more complicated to explain. Guided by the principle of parsimony, a data analyst therefore may naturally be reluctant to move beyond an additive model unless it is truly warranted. To put this principle of interaction reluctance into practice, we formulate the problem as a hypothesis test with a fitted sparse additive model (SPAM) serving as the null. Because our hypotheses on interaction effects are formed after fitting a SPAM to the data, we adopt a selective inference approach to construct p-values that properly account for this data adaptivity. Our approach makes use of external randomization to obtain the distribution of test statistics conditional on the SPAM fit, allowing us to derive valid p-values, corrected for the over-optimism introduced by the data-adaptive process prior to the test. Through experiments on simulated and real data, we illustrate that--even with small amounts of external randomization--this rigorous modeling approach enjoys considerable advantages over naive methods and data splitting.

Problem

• Testing interaction effects after fitting additive models
• Addressing over-optimism in data-adaptive hypothesis testing
• Validating interactions without compromising model interpretability

Innovation

• Uses sparse additive model (SPAM) as null hypothesis
• Applies selective inference for valid p-values
• Employs external randomization for test statistics