|Fr 25. November 2022
|Data streams are omnipresent. Think of sensor data, bank transactions, or stock movements. We assume that such data is generated according to an underlying distribution, which may change at so-called change points. These points signal events of interest; hence one wants to detect them.
A principled approach for finding such change points is to use maximum mean discrepancy (MMD) for a statistical hypothesis test, with the null hypothesis that the distribution does not change. However, the quadratic runtime of MMD prohibits its application in the streaming setting. Approximations for that setting exist but these suffer from high variance.
In the static setting, the so-called Nyström method allows to reduce the quadratic runtime of MMD with only a slight increase in variance. We propose an algorithm to employ Nyström estimators for MMD in the streaming setting and compare it to existing approximations.