New method detects changes in noisy dynamical systems with finite-sample guarantees

Aparna Rajput has published a new paper on arXiv (2606.06785) addressing finite-sample change detection in noisy one-dimensional dynamical systems. The method works by partitioning the state space, estimating a finite transition matrix from observed transitions, and applying a small Doeblin-type regularization to ensure a unique stationary distribution. It then computes an empirical stationary distribution for a reference segment and compares it to distributions from later sliding windows using an L1 distance score. Large scores indicate a change in stationary behavior. The paper provides explicit finite-sample bounds that separate sampling error, regularization bias, partition approximation error, and noise bias. It also offers a single-window false-alarm guarantee and a sufficient detection condition when the invariant density changes by more than the estimation error. The method is illustrated on synthetic noisy beta-map change-point experiments.

The work sits at the intersection of machine learning, dynamical systems, and statistics. While the method focuses on one-dimensional systems, it provides a rigorous foundation for change detection in settings where traditional approaches may fail due to noise or non-linearity. By offering finite-sample guarantees rather than asymptotic results, the approach is particularly relevant for practical applications where data lengths are limited. The explicit bounds and regularization technique make the method interpretable and potentially extensible to higher-dimensional systems. For professionals in time series analysis, anomaly detection, or system monitoring, this paper offers a principled way to detect distributional shifts in complex, noisy environments.