# Efficient Regression Models for Scan Statistics

arXiv: https://arxiv.org/abs/2608.22201 · HTML: https://mlsanity.com/paper/2608.22201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 63 references that are in the map.
- First posted on arXiv 23 Aug 2026.

## Builds on (most cited first, 7 of 7)

- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guarantees](https://mlsanity.com/paper/1804.09893/) (2018)
- [When Model Meets New Normals: Test-time Adaptation for Unsupervised Time-series Anomaly Detection](https://mlsanity.com/paper/2312.11976/) (2023)
- [Multiple Change-point Detection: a Selective Overview](https://mlsanity.com/paper/1512.04093/) (2015)
- [Near-optimal Anomaly Detection in Graphs using Lovasz Extended Scan Statistic](https://mlsanity.com/paper/1312.3291/) (2013)
- [Quantifying and Reducing Bias in Maximum Likelihood Estimation of Structured Anomalies](https://mlsanity.com/paper/2007.07878/) (2020)
- [Localising change points in piecewise polynomials of general degrees](https://mlsanity.com/paper/2007.09910/) (2020)

## Abstract (arXiv)

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(n4) 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.