Distribution-Free Predictive Inference under Unknown Temporal Drift

TL;DR

This paper introduces an adaptive method for distribution-free predictive inference that accounts for unknown temporal drift by selecting an optimal data window, ensuring reliable uncertainty quantification in changing environments.

Contribution

It proposes a novel adaptive window selection strategy based on bias-variance tradeoff to maintain valid prediction sets under unknown temporal drift.

Findings

Provides sharp coverage guarantees for the proposed method.

Demonstrates effectiveness through synthetic and real data experiments.

Abstract

Distribution-free prediction sets play a pivotal role in uncertainty quantification for complex statistical models. Their validity hinges on reliable calibration data, which may not be readily available as real-world environments often undergo unknown changes over time. In this paper, we propose a strategy for choosing an adaptive window and use the data therein to construct prediction sets. The window is selected by optimizing an estimated bias-variance tradeoff. We provide sharp coverage guarantees for our method, showing its adaptivity to the underlying temporal drift. We also illustrate its efficacy through numerical experiments on synthetic and real data.