Nested conformal prediction and quantile out-of-bag ensemble methods

TL;DR

This paper introduces a unified nested set framework for conformal prediction, extending existing methods to ensemble and out-of-bag techniques, and proposes a new algorithm, QOOB, which demonstrates strong empirical performance.

Contribution

It provides a novel nested sets perspective on conformal prediction, enabling seamless integration of various nonconformity scores and aggregation schemes, and introduces the QOOB algorithm combining multiple advanced ideas.

Findings

QOOB performs best or near best on diverse datasets.

The nested framework unifies different conformal prediction methods.

Efficient implementation of cross-conformal methods is achieved.

Abstract

Conformal prediction is a popular tool for providing valid prediction sets for classification and regression problems, without relying on any distributional assumptions on the data. While the traditional description of conformal prediction starts with a nonconformity score, we provide an alternate (but equivalent) view that starts with a sequence of nested sets and calibrates them to find a valid prediction set. The nested framework subsumes all nonconformity scores, including recent proposals based on quantile regression and density estimation. While these ideas were originally derived based on sample splitting, our framework seamlessly extends them to other aggregation schemes like cross-conformal, jackknife+ and out-of-bag methods. We use the framework to derive a new algorithm (QOOB, pronounced cube) that combines four ideas: quantile regression, cross-conformalization, ensemble methods and out-of-bag predictions. We develop a computationally efficient implementation of cross-conformal, that is also used by QOOB. In a detailed numerical investigation, QOOB performs either the best or close to the best on all simulated and real datasets. Code for QOOB is available at https://github.com/aigen/QOOB.