  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.
