On computing correlated aggregates over continual data streams

In many applications from telephone fraud detection to network management, data arrives in a stream, and there is a need to maintain a variety of statistical summary information about a large number of customers in an online fashion. At present, such applications maintain basic aggregates such as running extrema values (MIN, MAX), averages, standard deviations, etc., that can be computed over data streams with limited space in a straightforward way. However, many applications require knowledge of more complex aggregates relating different attributes, so-called correlated aggregates. As an example, one might be interested in computing the percentage of international phone calls that are longer than the average duration of a domestic phone call. Exact computation of this aggregate requires multiple passes over the data stream, which is infeasible.