Flexible Conformal Highest Predictive Conditional Density Sets

TL;DR

The paper introduces conformal highest conditional density sets (CHCDS), a method for constructing prediction sets with guaranteed coverage, especially effective in multi-modal error scenarios, validated through simulations and real data.

Contribution

It proposes a novel conformal prediction method that leverages estimated conditional densities, with proven validity and negligible adjustment under correct specification.

Findings

CHCDS outperforms existing methods in multi-modal error scenarios.

CHCDS matches existing methods in unimodal error cases.

The method guarantees nominal coverage even with model misspecification.

Abstract

We introduce our method, conformal highest conditional density sets (CHCDS), that forms conformal prediction sets using existing estimated conditional highest density predictive regions. We prove the validity of the method, and that conformal adjustment is negligible under some regularity conditions. In particular, if we correctly specify the underlying conditional density estimator, the conformal adjustment will be negligible. The conformal adjustment, however, always provides guaranteed nominal unconditional coverage, even when the underlying model is incorrectly specified. We compare the proposed method via simulation and a real data analysis to other existing methods. Our numerical results show that CHCDS is better than existing methods in scenarios where the error term is multi-modal, and just as good as existing methods when the error terms are unimodal.