Non-partitioned e-detectors for nonparametric sequential change detection

arXiv:2607.28322 · stat.ME, math.ST, stat.ML · Submitted 2026-07-30 · Read on arXiv

Aytijhya Saha, Aaditya Ramdas

stat.ME, math.ST, stat.ML

Submitted: 2026-07-30

Code: https://github.com/Aytijhya/Nonseparated-e-detector

License: http://creativecommons.org/licenses/by/4.0/

The gist: We study the problem of sequential change detection over a general class of probability distributions (P), where both the pre-change and post-change distributions are unknown and belong to P.

Terminology

Abstract

We study the problem of sequential change detection over a general class of probability distributions (P), where both the pre-change and post-change distributions are unknown and belong to P. We do not assume a pre-specified partition of P into pre- and post-change families. We propose a general class of sequential change detectors obtained by aggregating point-null e-processes over possible changepoints and taking an infimum over candidate no-change distributions. The weights in the aggregation scheme determine whether they attain average run length (ARL) control and probability-of-false-alarm (PFA) control. Under suitable assumptions, we prove that our methods achieve first-order asymptotically optimal detection delay. Concrete examples include sub-Gaussian and bounded mean changes, Gaussian mean changes with unknown variance, as well as changes in Markov transition matrices.

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