Distribution-free Conformal Prediction for Ordinal Classification

TL;DR

This paper develops distribution-free conformal prediction methods tailored for ordinal classification, ensuring valid coverage and improved performance over existing methods through theoretical guarantees and empirical validation.

Contribution

It introduces new conformal prediction techniques for ordinal data that achieve marginal and class-specific coverage with theoretical guarantees.

Findings

Methods achieve satisfactory marginal and conditional coverage.

Simulation and real data show improved performance.

Proposes contiguous and non-contiguous prediction sets.

Abstract

Conformal prediction is a general distribution-free approach for constructing prediction sets combined with any machine learning algorithm that achieve valid marginal or conditional coverage in finite samples. Ordinal classification is common in real applications where the target variable has natural ordering among the class labels. In this paper, we discuss constructing distribution-free prediction sets for such ordinal classification problems by leveraging the ideas of conformal prediction and multiple testing with FWER control. Newer conformal prediction methods are developed for constructing contiguous and non-contiguous prediction sets based on marginal and conditional (class-specific) conformal $p$-values, respectively. Theoretically, we prove that the proposed methods respectively achieve satisfactory levels of marginal and class-specific conditional coverages. Through simulation study and real data analysis, these proposed methods show promising performance compared to the existing conformal method.