Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models

Recent methods for training generalized additive models (GAMs) with pairwise interactions achieve state-of-the-art accuracy on a variety of datasets. Adding interactions to GAMs, however, introduces an identifiability problem: effects can be freely moved between main effects and interaction effects without changing the model predictions. In some cases, this can lead to contradictory interpretations of the same underlying function. This is a critical problem because a central motivation of GAMs is model interpretability. In this paper, we use the Functional ANOV A decomposition to uniquely define interaction effects and thus produce identifiable additive models with purified interactions. To compute this decomposition, we present a fast, exact, mass-moving algorithm that transforms any piecewise-constant function (such as a tree-based model) into a purified, canonical representation. We apply this algorithm to several datasets and show large disparity, including contradictions, between the apparent and the purified effects. An important question in data analysis is whether two variables act in concert to affect an outcome. But this unconstrained additive model has fundamental flaws.