Efficient Regression Models for Scan Statistics

Abstract:We introduce a new class of regression models for scan statistics on real-valued signals. These allow for improved fitting of non-stationary signals to contrast with the interval anomalies identified by the scan statistics. Our models can represent generalized likelihood ratio statistics. While these methods naively require $O(n^4)$ for a length $n$ signal, we provide algorithmic improvements which lead to linear time algorithms (with assumptions on max interval width). Our methods, especially ones based on Nadaraya-Watson kernel regression, are demonstrated as especially effective in detecting both synthetically planted anomalies, and for identifying a real ``platforming'' issue in interferometric astronomy.

Methodology (stat.ME); Machine Learning (cs.LG)

arXiv:2608.22201 [stat.ME]

(or arXiv:2608.22201v1 [stat.ME] for this version)

https://doi.org/10.48550/arXiv.2608.22201 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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