Flexible Conformal Highest Predictive Conditional Density Sets

Max Sampson; Kung-Sik Chan

doi:10.48550/arxiv.2406.18052

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Flexible Conformal Highest Predictive Conditional Density Sets

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Flexible Conformal Highest Predictive Conditional Density Sets

Max Sampson and Kung-Sik Chan

arXiv.org

Cornell University

06/26/2024

DOI: 10.48550/arxiv.2406.18052

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https://doi.org/10.48550/arxiv.2406.18052View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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. When the underlying model is incorrect, the conformal adjustment provides guaranteed nominal unconditional coverage. We compare the proposed method via simulation and a real data analysis to other existing methods. Our numerical results show that the flexibility of being able to use any existing conditional density estimation method is a large advantage for CHCDS compared to existing methods.

Mathematics - Statistics Theory

Statistics - Methodology

Statistics - Theory

Details

Title: Subtitle: Flexible Conformal Highest Predictive Conditional Density Sets
Creators: Max Sampson
Kung-Sik Chan
Resource Type: Preprint
Publication Details: arXiv.org
DOI: 10.48550/arxiv.2406.18052
eISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 06/26/2024
Academic Unit: Statistics and Actuarial Science; Radiology
Record Identifier: 9984649154702771

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