Localized Conformal Multi-Quantile Regression

TL;DR

This paper introduces Localized Conformal Multi-Quantile Regression (LCMQR), a new method that creates adaptive prediction intervals by combining multi-quantile data with kernel-based localization, improving efficiency and validity in heterogeneous environments.

Contribution

The paper proposes LCMQR, resolving an inconsistency in prior methods and extending it to group-calibrated versions for subpopulation validity, advancing conformal prediction techniques.

Findings

LCMQR achieves superior efficiency on benchmark datasets.

GC-LCMQR guarantees finite-sample validity within subgroups.

Theoretical proof shows tighter intervals with the new scoring mechanism.

Abstract

Standard conformal prediction methods guarantee marginal coverage but often produce inefficient intervals that fail to adapt to local heteroscedasticity, while recent localized approaches often struggle to maintain validity across distinct subpopulations with varying noise profiles. To address these challenges, we introduce Localized Conformal Multi-Quantile Regression (LCMQR), a novel framework that synergizes multi-quantile information with kernel-based localization to construct efficient and adaptive prediction intervals. Theoretically, we resolve an inconsistency in Conformalized Composite Quantile Regression (CCQR) by proving that our consistent Average-then-Max scoring mechanism systematically yields tighter intervals than the Max-then-Average approach used in prior work. For heterogeneous environments, we extend this framework to Group-Calibrated LCMQR (GC-LCMQR) via a stratified calibration step that guarantees finite-sample validity within distinct subgroups. Experiments on benchmark datasets and an Individual Treatment Effect (ITE) task demonstrate that LCMQR achieves superior efficiency on standard benchmarks, while GC-LCMQR uniquely achieves group-level coverage for target subgroups in mixture populations where baselines fail.