Alternating Pruned Dynamic Programming for Multiple Epidemic Change-Point Estimation

Abstract

In this article, 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 nontrivial 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. Supplementary material for this article is available online.

KEYWORDS:

• Change-point
• DNA copy number variation
• Epidemic alternative
• Model selection
• Multiple testing

Supplementary Materials

The supplementary material contains additional simulation, real data application and technical proofs. It also contains the R codes to reproduce the numerical results presented in the paper.

Acknowledgments

The authors thank the associate editor and two anonymous referees for their comments that helped improve the quality and presentation of the article.

Funding

Zhao’s research is supported in part by National Science Foundation grant DMS-2014053. Yau’s research is supported in part by grants from HKSAR-RGC-GRF 14302719 and 14305517.

Note

¹ For example, consider a sequence that has the following alternating state changes: a high (epidemic) state $\to$ the normal state $\to$ a low (epidemic) state $\to$ the normal state $\to$ another high (epidemic) state.