Sketching Aggregates over Probabilistic Streams

The datastream model of computation has proven a valuable tool in developing algorithms for processing large amounts of data in small space. This survey examines an extension of this model that deals with uncertain data, called the probabilistic stream model. As in the standard setting, we are presented with a stream of items, with no random access to the data. However, each item is represented by a probability distribution function, allowing us to model the uncertainty associated with each element. We examine the computation of several aggregates in the probabilistic stream setting, including the frequency moments of the stream, average, minimum, and quantiles. The key difficulty in these computations is the fact that the stream represents an exponential number of possible worlds, and even simple numbers like the length of the stream can be different in different possible worlds. Obtaining accurate, reliable estimates can be very non-trivial.