  In many applications, monitoring area under the ROC curve (AUC) in a sliding
window over a data stream is a natural way of detecting changes in the system.
The drawback is that computing AUC in a sliding window is expensive, especially
if the window size is large and the data flow is significant.
  In this paper we propose a scheme for maintaining an approximate AUC in a
sliding window of length $k$. More specifically, we propose an algorithm that,
given $\epsilon$, estimates AUC within $\epsilon / 2$, and can maintain this
estimate in $O((\log k) / \epsilon)$ time, per update, as the window slides.
This provides a speed-up over the exact computation of AUC, which requires
$O(k)$ time, per update. The speed-up becomes more significant as the size of
the window increases. Our estimate is based on grouping the data points
together, and using these groups to calculate AUC. The grouping is designed
carefully such that ($i$) the groups are small enough, so that the error stays
small, ($ii$) the number of groups is small, so that enumerating them is not
expensive, and ($iii$) the definition is flexible enough so that we can
maintain the groups efficiently.
  Our experimental evaluation demonstrates that the average approximation error
in practice is much smaller than the approximation guarantee $\epsilon / 2$,
and that we can achieve significant speed-ups with only a modest sacrifice in
accuracy.
