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Highest Probability Density Conformal Regions
Dataset   Open access

Highest Probability Density Conformal Regions

Max Sampson and Kung-Sik Chan
Taylor & Francis
06/23/2025
DOI: 10.6084/m9.figshare.29385259
url
https://doi.org/10.6084/m9.figshare.29385259View
Open Access

Abstract

This paper proposes a new method for finding the highest predictive density set or region, within the heteroscedastic regression framework. This framework enjoys the property that any highest predictive density set is a translation of some scalar multiple of a highest density set for the standardized regression error, with the same prediction accuracy. The proposed method leverages this property to efficiently compute conformal prediction regions using signed conformal inference and kernel density estimation, in conjunction with any conditional mean and scale estimators. While most conformal prediction methods output prediction intervals, this method adapts to the target. When the target is multi-modal, the proposed method outputs an approximation of the smallest multi-modal set. When the target is uni-modal, the proposed method outputs an approximation of the smallest interval. Under mild regularity conditions, we show that these conformal prediction sets are asymptotically close to the true smallest prediction sets. Because of the conformal guarantee, even in finite sample sizes the method has guaranteed coverage. With simulations and a real data analysis we demonstrate that the proposed method is better than existing methods when the target is multi-modal or strongly heteroscedastic, and gives similar results in other scenarios. Supplementary Materials, including proofs, code, and additional comments, are available online.
Biochemistry Biophysics Biotechnology Computational Biology Microbiology Biological Sciences not elsewhere classified FOS: Biological sciences Information Systems not elsewhere classified Mathematical Sciences not elsewhere classified Medicine

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