Distribution-Free Predictive Inference under Unknown Temporal Drift
This work addresses uncertainty quantification for statistical models in dynamic real-world environments, representing an incremental improvement by adapting to temporal drift.
The paper tackles the problem of constructing distribution-free prediction sets under unknown temporal drift by proposing an adaptive window selection strategy that optimizes a bias-variance tradeoff, achieving sharp coverage guarantees and demonstrating efficacy in numerical experiments.
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.