# Minimax-Optimal Algorithms for Detecting Changes in Statistically Periodic Random Processes

## TL;DR

This paper introduces minimax-optimal algorithms for detecting changes in statistically periodic random processes, with applications to real-world datasets like social media activity during events.

## Contribution

It proposes a new class of stochastic processes for modeling periodicity and develops algorithms that are asymptotically optimal for change detection in these processes.

## Key findings

- Algorithms achieve minimax asymptotic optimality as false alarm rate approaches zero.
- Developed methods handle unknown post-change distributions and multiple observation streams.
- Applied algorithms successfully to detect a running event from Instagram data.

## Abstract

Theory and algorithms are developed for detecting changes in the distribution of statistically periodic random processes. The statistical periodicity is modeled using independent and periodically identically distributed processes, a new class of stochastic processes proposed by us. An algorithm is developed that is minimax asymptotically optimal as the false alarm rate goes to zero. Algorithms are also developed for the cases when the post-change distribution is not known or when there are multiple streams of observations. The modeling is inspired by real datasets encountered in cyber-physical systems, biology, and medicine. The developed algorithms are applied to sequences of Instagram counts collected around a 5K run in New York City to detect the run.