  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 outbreaks by detecting signs of changes
in the cases. 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. 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 37 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 basic reproduction number $R0$ and the timing of
social distancing. The results showed that our method can effectively monitor
the dynamics of $R0$, and confirmed the effectiveness of social distancing at
containing the epidemic in a region. We conclude that our method is a promising
approach to the pandemic 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
