GapTV: Accurate and Interpretable Low-Dimensional Regression and Classification
This work addresses the need for interpretable models in low-dimensional settings where existing methods like CART and CRISP fall short, representing an incremental improvement in this domain-specific area.
The authors tackled the problem of interpretable regression and classification with few features, where linear or additive models are insufficient, by introducing GapTV, which partitions the feature space into constant-value blocks and optimizes them jointly. They demonstrated that GapTV achieves a better accuracy-interpretability trade-off than CART and CRISP, though no specific numerical gains are provided.
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.