Title: Interpretable Low-Dimensional Regression via Data-Adaptive Smoothing,
Abstract: 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 Maximum
Variance Total Variation denoising (MVTV), 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. MVTV 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 via both a
complexity-accuracy tradeoff metric and a human study, demonstrating that that
MVTV is a more powerful and interpretable method.