# Distribution-Free Predictive Inference under Unknown Temporal Drift

arXiv: https://arxiv.org/abs/2406.06516 · HTML: https://mlsanity.com/paper/2406.06516/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 30 of 34)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Doubly Robust Calibration of Prediction Sets under Covariate Shift](https://mlsanity.com/paper/2203.01761/) (2022)
- [Conformal Prediction with Temporal Quantile Adjustments](https://mlsanity.com/paper/2205.09940/) (2022)
- [Prediction Sets Adaptive to Unknown Covariate Shift](https://mlsanity.com/paper/2203.06126/) (2022)
- [PAC Confidence Predictions for Deep Neural Network Classifiers](https://mlsanity.com/paper/2011.00716/) (2020)
- [PAC Prediction Sets Under Label Shift](https://mlsanity.com/paper/2310.12964/) (2023)
- [An Adaptive Algorithm for Learning with Unknown Distribution Drift](https://mlsanity.com/paper/2305.02252/) (2023)
- [JAWS: Auditing Predictive Uncertainty Under Covariate Shift](https://mlsanity.com/paper/2207.10716/) (2022)
- [Group-Weighted Conformal Prediction](https://mlsanity.com/paper/2401.17452/) (2024)
- [Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series](https://mlsanity.com/paper/2402.05203/) (2024)
- [Model Assessment and Selection under Temporal Distribution Shift](https://mlsanity.com/paper/2402.08672/) (2024)
- [Learning with a Drifting Target Concept](https://mlsanity.com/paper/1505.05215/) (2015)

## Abstract (arXiv)

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.