GapTV: Accurate and Interpretable Low-Dimensional Regression and Classification

We consider the problem of estimating a regression function in the common situation where the number of features is small, where interpretability of the model is a high priority, and where simple linear or additive models fail to provide adequate performance. To address this problem, we present GapTV, an approach that is conceptually related both to CART and to the more recent CRISP algorithm, a state-of-the-art alternative method for interpretable nonlinear regression. GapTV divides the feature space into blocks of constant value and fits the value of all blocks jointly via a convex optimization routine. Our method is fully data-adaptive, in that it incorporates highly robust routines for tuning all hyperparameters automatically. We compare our approach against CART and CRISP and demonstrate that GapTV finds a much better trade-off between accuracy and interpretability.