Change detection with conformal martingales: new optimal constructions, and suboptimality of existing methods

arXiv:2609.27179 · math.ST, stat.ME, stat.ML, stat.TH · Submitted 2026-09-23 · Read on arXiv

math.ST, stat.ME, stat.ML, stat.TH

Submitted: 2026-09-23

Updated: 2026-09-23

Comments: 76 pages, 6 figures;

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Conformal Test Martingale — 17× in this paper
• Distribution Shift — 8× in this paper · explained in 5 episodes
• Minimax optimality — 8× in this paper · explained in 2 episodes
• Calibration — 7× in this paper · explained in 7 episodes
• Exchangeability — 6× in this paper · explained in 2 episodes
• Monte Carlo — 6× in this paper
• Consistency — 4× in this paper · explained in 3 episodes
• Score Function — 4× in this paper · explained in 4 episodes
• Benchmark — 3× in this paper · explained in 2 episodes
• Embeddings — 3× in this paper · explained in 2 episodes
• Adaptive Monitoring — 2× in this paper · explained in 1 episode
• Aggregation — 2× in this paper · explained in 1 episode
• Concept Drift — 1× in this paper · explained in 4 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Pairwise Comparisons — 1× in this paper · explained in 2 episodes
• Pruning — 1× in this paper · explained in 4 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• A complete characterization of sequential testability and change detectability in i.i.d. models
• Online Kernel CUSUM for Change-Point Detection

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