# Robust Conformal Prediction under Distribution Shift via Physics-Informed Structural Causal Model

arXiv: https://arxiv.org/abs/2403.15025 · HTML: https://mlsanity.com/paper/2403.15025/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 22 Mar 2024.

## Builds on (most cited first, 10 of 10)

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecasting](https://mlsanity.com/paper/1802.07007/) (2018)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Probabilistically robust conformal prediction](https://mlsanity.com/paper/2307.16360/) (2023)
- [Stable Conformal Prediction Sets](https://mlsanity.com/paper/2112.10224/) (2021)

## Built on by (most cited first, 1 of 1)

- [Power Interpretable Causal ODE Networks: A Unified Model for Explainable Anomaly Detection and Root Cause Analysis in Power Systems](https://mlsanity.com/paper/2602.12592/) (2026)

## Abstract (arXiv)

Uncertainty is critical to reliable decision-making with machine learning. Conformal prediction (CP) handles uncertainty by predicting a set on a test input, hoping the set to cover the true label with at least (1-α) confidence. This coverage can be guaranteed on test data even if the marginal distributions PX differ between calibration and test datasets. However, as it is common in practice, when the conditional distribution PY|X is different on calibration and test data, the coverage is not guaranteed and it is essential to measure and minimize the coverage loss under distributional shift at textitall possible confidence levels. To address these issues, we upper bound the coverage difference at all levels using the cumulative density functions of calibration and test conformal scores and Wasserstein distance. Inspired by the invariance of physics across data distributions, we propose a physics-informed structural causal model (PI-SCM) to reduce the upper bound. We validated that PI-SCM can improve coverage robustness along confidence level and test domain on a traffic speed prediction task and an epidemic spread task with multiple real-world datasets.