# GapTV: Accurate and Interpretable Low-Dimensional Regression and Classification

## TL;DR

GapTV is a novel method for low-dimensional regression and classification that offers a better balance of accuracy and interpretability by dividing the feature space into blocks and fitting them jointly through convex optimization.

## Contribution

It introduces GapTV, a data-adaptive, interpretable model that improves upon CART and CRISP in accuracy-interpretability trade-offs for low-dimensional problems.

## Key findings

- GapTV outperforms CART and CRISP in accuracy and interpretability.
- The method automatically tunes hyperparameters robustly.
- GapTV provides a better trade-off between accuracy and interpretability.

## 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 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.