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Software

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 $$64\%$$ 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.

This paper addresses the issue of how we can detect changes of changes, which we call metachanges, in data streams. A metachange refers to a change in patterns of when and how changes occur, referred to as “metachanges along time” and “metachanges along state”, respectively. Metachanges along time mean that the intervals between change points significantly vary, whereas metachanges along state mean that the magnitude of changes varies. It is practically important to detect metachanges because they may be early warning signals of important events. This paper introduces a novel notion of metachange statistics as a measure of the degree of a metachange. The key idea is to integrate metachanges along both time and state in terms of “code length” according to the minimum description length (MDL) principle. We develop an online metachange detection algorithm (MCD) based on the statistics to apply it to a data stream. With synthetic datasets, we demonstrated that MCD detects metachanges earlier and more accurately than existing methods. With real datasets, we demonstrated that MCD can lead to the discovery of important events that might be overlooked by conventional change detection methods.

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