# Single Trajectory Conformal Prediction

arXiv: https://arxiv.org/abs/2406.01570 · HTML: https://mlsanity.com/paper/2406.01570/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 3 Jun 2024.

## Builds on (most cited first, 30 of 32)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [On the optimality of the Hedge algorithm in the stochastic regime](https://mlsanity.com/paper/1809.01382/) (2018)
- [Learning with little mixing](https://mlsanity.com/paper/2206.08269/) (2022)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Least-Squares Temporal Difference Learning for the Linear Quadratic Regulator](https://mlsanity.com/paper/1712.08642/) (2017)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Single Trajectory Nonparametric Learning of Nonlinear Dynamics](https://mlsanity.com/paper/2202.08311/) (2022)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Localized Adaptive Risk Control](https://mlsanity.com/paper/2405.07976/) (2024)
- [Physics Constrained Motion Prediction with Uncertainty Quantification](https://mlsanity.com/paper/2302.01060/) (2023)
- [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023)
- [Relaxing the I.I.D. Assumption: Adaptively Minimax Optimal Regret via Root-Entropic Regularization](https://mlsanity.com/paper/2007.06552/) (2020)
- [Extending Conformal Prediction to Hidden Markov Models with Exact Validity via de Finetti's Theorem for Markov Chains](https://mlsanity.com/paper/2210.02271/) (2022)
- [Randomization Tests for Adaptively Collected Data](https://mlsanity.com/paper/2301.05365/) (2023)

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

- [Distribution-Free Predictive Inference under Unknown Temporal Drift](https://mlsanity.com/paper/2406.06516/) (2024)

## Abstract (arXiv)

We study the performance of risk-controlling prediction sets (RCPS), an empirical risk minimization-based formulation of conformal prediction, with a single trajectory of temporally correlated data from an unknown stochastic dynamical system. First, we use the blocking technique to show that RCPS attains performance guarantees similar to those enjoyed in the iid setting whenever data is generated by asymptotically stationary and contractive dynamics. Next, we use the decoupling technique to characterize the graceful degradation in RCPS guarantees when the data generating process deviates from stationarity and contractivity. We conclude by discussing how these tools could be used toward a unified analysis of online and offline conformal prediction algorithms, which are currently treated with very different tools.