Regression Trees for Fast and Adaptive Prediction Intervals

TL;DR

elsarticle.cls provides a robust LaTeX document class tailored for Elsevier journals, addressing the need for consistent formatting and reduced package conflicts. It is built on article.cls and depends on standard packages (natbib, geometry, fleqn, graphicx, endfloat, hyperref, amsthm), enabling stable compilation and minimal clashes. The paper outlines major differences from the older elsart.cls, notably avoiding redefinitions that cause conflicts and offering flexible publication formats (preprint, final, model variants) and enhanced front matter handling. It also documents practical features such as author-affiliation linking, long title support, theorem environments, and amsthm compatibility to streamline academic writing. Installation guidance via Elsevier resources and CTAN provides a clear path to obtaining and deploying the class within the standard TeX Live/MiKTeX distributions, improving submission workflow.

Abstract

Predictive models make mistakes. Hence, there is a need to quantify the uncertainty associated with their predictions. Conformal inference has emerged as a powerful tool to create statistically valid prediction regions around point predictions, but its naive application to regression problems yields non-adaptive regions. New conformal scores, often relying upon quantile regressors or conditional density estimators, aim to address this limitation. Although they are useful for creating prediction bands, these scores are detached from the original goal of quantifying the uncertainty around an arbitrary predictive model. This paper presents a new, model-agnostic family of methods to calibrate prediction intervals for regression problems with local coverage guarantees. Our approach is based on pursuing the coarsest partition of the feature space that approximates conditional coverage. We create this partition by training regression trees and Random Forests on conformity scores. Our proposal is versatile, as it applies to various conformity scores and prediction settings and demonstrates superior scalability and performance compared to established baselines in simulated and real-world datasets. We provide a Python package clover that implements our methods using the standard scikit-learn interface.