Flexible distribution-free conditional predictive bands using density estimators

TL;DR

This paper introduces two new conformal methods, Dist-split and CD-split, that use density estimators to achieve asymptotic conditional coverage without strong dependence assumptions, offering more accurate and interpretable prediction bands.

Contribution

The paper proposes novel conformal methods based on density estimators that attain asymptotic conditional coverage without relying on dependence assumptions, improving coverage control and interval interpretability.

Findings

Methods outperform previous approaches in coverage control.

CD-split produces smaller, local prediction regions.

Both methods show better coverage and shorter intervals in simulations.

Abstract

Conformal methods create prediction bands that control average coverage under no assumptions besides i.i.d. data. Besides average coverage, one might also desire to control conditional coverage, that is, coverage for every new testing point. However, without strong assumptions, conditional coverage is unachievable. Given this limitation, the literature has focused on methods with asymptotical conditional coverage. In order to obtain this property, these methods require strong conditions on the dependence between the target variable and the features. We introduce two conformal methods based on conditional density estimators that do not depend on this type of assumption to obtain asymptotic conditional coverage: Dist-split and CD-split. While Dist-split asymptotically obtains optimal intervals, which are easier to interpret than general regions, CD-split obtains optimal size regions, which are smaller than intervals. CD-split also obtains local coverage by creating a data-driven partition of the feature space that scales to high-dimensional settings and by generating prediction bands locally on the partition elements. In a wide variety of simulated scenarios, our methods have a better control of conditional coverage and have smaller length than previously proposed methods.