Interpretable Low-Dimensional Regression via Data-Adaptive Smoothing
It addresses interpretable regression for domains needing simple models, but appears incremental as it builds on existing methods like CRISP.
The paper tackles the problem of estimating a regression function with few features where interpretability is crucial, by introducing MVTV, a method that divides feature space into constant-value blocks and fits them via convex optimization, showing it outperforms CART and CRISP in power and interpretability.
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.