On the Detection of Concept Changes in Time-Varying Data Stream by Testing Exchangeability

Introduction In a data streaming setting, data points are observed one by one. The concepts to be learned from the data points may change infinitely often as the data is streaming. We extend the idea of testing exchangeability online [2] to a martingale framework to detect concept changes in time-varying data streams [P1]. •Two martingale tests using: (i) martingale values (MT1) and (ii) the martingale difference (MT2) [P1] are proposed. •MT1 is shown to be an approximation of the sequential probability ratio test (SPRT). The relationship between the threshold value used and its size and power is deduced. The mean delay time before a change is detected is estimated. •Under some assumptions, MT2 theoretically has a lower probability than MT1 of rejecting the null hypothesis, “no concept change in the data stream”, when it is in fact correct [P1].