Title: Reluctant Interaction Inference after Additive Modeling Show Chinese title

Title: 加性建模后的勉强交互推断

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. Show Chinese abstract

Abstract: 加性模型兼具非线性模型的灵活性，同时仍然易于被人类理解。相比之下，涉及特征交互的其他非线性模型不仅更难拟合，而且在解释上也更加复杂。遵循简约原则，数据分析师自然可能不愿意超出加性模型，除非确实必要。为了将这种交互抗拒的原则付诸实践，我们将问题构建成一个假设检验，其中拟合的稀疏加性模型（SPAM）作为原假设。由于我们关于交互效应的假设是在拟合SPAM到数据之后形成的，因此我们采用选择性推断方法来构造p值，以正确考虑这种数据适应性。我们的方法利用外部随机化来获得测试统计量在给定SPAM拟合下的分布，从而允许我们推导出有效的p值，并修正由测试前的数据自适应过程引入的过度乐观偏差。通过在模拟数据和真实数据上的实验，我们展示了——即使使用少量的外部随机化——这种严格的建模方法相对于简单方法和数据分割方法具有显著优势。