# Monitoring for Shifts at Unknown Times: Parameter-Free Conditional Conformal Martingales

arXiv: https://arxiv.org/abs/2610.17343 · HTML: https://mlsanity.com/paper/2610.17343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 51 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Coin Betting and Parameter-Free Online Learning](https://mlsanity.com/paper/1602.04128/) (2016)
- [Black-Box Reductions for Parameter-free Online Learning in Banach Spaces](https://mlsanity.com/paper/1802.06293/) (2018)
- [Strongly Adaptive Online Learning](https://mlsanity.com/paper/1502.07073/) (2015)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [There are natural scores: Full comment on Shafer, "Testing by betting: A strategy for statistical and scientific communication"](https://mlsanity.com/paper/2102.05569/) (2021)
- [Admissible anytime-valid sequential inference must rely on nonnegative martingales](https://mlsanity.com/paper/2009.03167/) (2020)
- [Tight Concentrations and Confidence Sequences from the Regret of Universal Portfolio](https://mlsanity.com/paper/2110.14099/) (2021)
- [Tracking the risk of a deployed model and detecting harmful distribution shifts](https://mlsanity.com/paper/2110.06177/) (2021)
- [Testing randomness](https://mlsanity.com/paper/1906.09256/) (2019)
- [Testing exchangeability: fork-convexity, supermartingales, and e-processes](https://mlsanity.com/paper/2102.00630/) (2021)
- [Retrain or not retrain: Conformal test martingales for change-point detection](https://mlsanity.com/paper/2102.10439/) (2021)
- [E-detectors: a nonparametric framework for sequential change detection](https://mlsanity.com/paper/2203.03532/) (2022)
- [Inductive Conformal Martingales for Change-Point Detection](https://mlsanity.com/paper/1706.03415/) (2017)
- [WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingales](https://mlsanity.com/paper/2505.04608/) (2025)
- [Online Learning for Changing Environments using Coin Betting](https://mlsanity.com/paper/1711.02545/) (2017)
- [Testing For Distribution Shifts with Conditional Conformal Test Martingales](https://mlsanity.com/paper/2602.13848/) (2026)
- [Switching Portfolios](https://mlsanity.com/paper/1301.7413/) (2013)
- [The power of forgetting in statistical hypothesis testing](https://mlsanity.com/paper/2402.06920/) (2024)

## Abstract (arXiv)

Conditional conformal test martingales provide sequential tests for detecting distribution shifts, using a fixed reference dataset to avoid contamination from test-time samples. Prior work used a penalized betting function via online optimization with smoothing, clipping, and other hyperparameters, which can adapt slowly when a shift occurs after a long stationary period. In this work, we introduce an approach that requires no hyperparameters and provably adapts quickly to shifts occurring at unknown times. Our key idea is to frame the penalized betting problem as portfolio selection in a three-asset market. Then, we use a restarting universal portfolio, with a heavy-tailed wealth allocation over time. We establish anytime false-alarm control and derive optimal finite-sample bounds on detection delay under detectable alternatives. We also develop an FFT-based implementation that computes the portfolio sequence over T rounds in O(T2ln T) time, instead of O(T3) of the naive implementation. Synthetic and real-world experiments suggest that the proposed approach adapts rapidly after long periods of null samples, with detection delays depending substantially less on shift time than prior baselines.