Accurate intelligible models with pairwise interactions

Standard generalized additive models (GAMs) usually model the dependent variable as a sum of univariate models. Although previous studies have shown that standard GAMs can be interpreted by users, their accuracy is significantly less than more complex models that permit interactions. In this paper, we suggest adding selected terms of interacting pairs of features to standard GAMs. The resulting models, which we call GA2{M}$-models, for Generalized Additive Models plus Interactions, consist of univariate terms and a small number of pairwise interaction terms. Since these models only include one- and two-dimensional components, the components of GA2M-models can be visualized and interpreted by users. To explore the huge (quadratic) number of pairs of features, we develop a novel, computationally efficient method called FAST for ranking all possible pairs of features as candidates for inclusion into the model. In a large-scale empirical study, we show the effectiveness of FAST in ranking candidate pairs of features. In addition, we show the surprising result that GA2M-models have almost the same performance as the best full-complexity models on a number of real datasets. Thus this paper postulates that for many problems, GA2M-models can yield models that are both intelligible and accurate.