Change Sign Detection with Differential MDL Change Statistics and its Applications to COVID-19 Pandemic Analysis.

We are concerned with the issue of detecting changes and their signs from a data stream. For example, when given time series of COVID-19 cases in a region, we may raise early warning signals of an epidemic by detecting signs of changes in the data. We propose a novel methodology to address this issue. The key idea is to employ a new information-theoretic notion, which we call the differential minimum description length change statistics (D-MDL), for measuring the scores of change sign. We first give a fundamental theory for D-MDL. We then demonstrate its effectiveness using synthetic datasets. We apply it to detecting early warning signals of the COVID-19 epidemic using time series of the cases for individual countries. We empirically demonstrate that D-MDL is able to raise early warning signals of events such as significant increase/decrease of cases. Remarkably, for about $64\%$ of the events of significant increase of cases in studied countries, our method can detect warning signals as early as nearly six days on average before the events, buying considerably long time for making responses. We further relate the warning signals to the dynamics of the basic reproduction number $R0$ and the timing of social distancing. The results show that our method is a promising approach to the epidemic analysis from a data science viewpoint. The software for the experiments is available at https://github.com/IbarakikenYukishi/differential-mdl-change-statistics. An online detection system is available at https://ibarakikenyukishi.github.io/d-mdl-html/index.html