DistMatch: Adaptive Binning via Distribution Matching for Robust Sequential Conformal Prediction

2026-05-30

AI Summary

This work addresses the non-exchangeability of residuals in time series data caused by temporal dependencies and distributional shifts. To tackle this challenge, the authors propose an adaptive binning mechanism that recursively partitions residuals using a binary tree constructed based on the Kolmogorov–Smirnov statistic, followed by quantile regression with online updates within each leaf node. This approach yields approximately exchangeable local residual sets without requiring reweighting, thereby enabling locally adaptive sequential conformal prediction. Empirical evaluations demonstrate that the method significantly outperforms existing approaches across diverse real-world and synthetic time series datasets, achieving higher coverage validity while producing substantially narrower prediction intervals.

Abstract

Sequential conformal prediction (CP) provides valid uncertainty quantification under the assumption of residual exchangeability. However, this assumption is often violated in real-world time series due to temporal dependencies and distributional shifts. While recent methods attempt to approximate exchangeability through reweighting, identifying optimal weights remains an open challenge. To address this limitation, we propose DistMatch, a binning-based method that recursively partitions residuals within a binary tree using the Kolmogorov-Smirnov (KS) statistic. We theoretically show that this partitioning induces approximately exchangeable leaves, thereby avoiding the need for reweighting. By applying quantile regression with online updates within each leaf, DistMatch enables locally adaptive inference and improves robustness to distributional shifts. Extensive experiments demonstrate that DistMatch outperforms existing sequential CP methods.

Problem

• sequential conformal prediction
• residual exchangeability
• distributional shifts
• temporal dependencies
• uncertainty quantification

Innovation

• adaptive binning
• distribution matching
• sequential conformal prediction
• Kolmogorov-Smirnov statistic
• quantile regression