Alternating Pruned Dynamic Programming for Multiple Epidemic Change-Point Estimation

TL;DR

This paper introduces an efficient algorithm for detecting multiple epidemic change-points in univariate sequences, explicitly modeling alternating normal and epidemic states, and demonstrates its superior accuracy and applicability across various fields.

Contribution

The paper proposes a novel two-stage alternating pruned dynamic programming algorithm that explicitly models the alternating structure of epidemic change-points, improving detection accuracy over classical methods.

Findings

Enhanced change-point detection accuracy compared to classical methods.

Efficient $O(n^2)$ algorithm for simultaneous inference on change-points and states.

Successful applications in DNA copy number variation and oceanographic studies.

Abstract

In this paper, we study the problem of multiple change-point detection for a univariate sequence under the epidemic setting, where the behavior of the sequence alternates between a common normal state and different epidemic states. This is a non-trivial generalization of the classical (single) epidemic change-point testing problem. To explicitly incorporate the alternating structure of the problem, we propose a novel model selection based approach for simultaneous inference on both change-points and alternating states. Using the same spirit as profile likelihood, we develop a two-stage alternating pruned dynamic programming algorithm, which conducts efficient and exact optimization of the model selection criteria and has $O(n^2)$ as the worst case computational cost. As demonstrated by extensive numerical experiments, compared to classical general-purpose multiple change-point detection procedures, the proposed method improves accuracy for both change-point estimation and model parameter estimation. We further show promising applications of the proposed algorithm to multiple testing with locally clustered signals, and demonstrate its advantages over existing methods in large scale multiple testing, in DNA copy number variation detection, and in oceanographic study.