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Estimating Aggregate Properties on Probabilistic Streams
The probabilistic-stream model was introduced by Jayram et al. \cite{JKV07}.
It is a generalization of the data stream model that is suited to handling
``probabilistic'' data where each item of the stream represents a probability
distribution over a set of possible events. Therefore, a probabilistic stream
determines a distribution over potentially a very large number of classical
"deterministic" streams where each item is deterministically one of the domain
values. The probabilistic model is applicable for not only analyzing streams
where the input has uncertainties (such as sensor data streams that measure
physical processes) but also where the streams are derived from the input data
by post-processing, such as tagging or reconciling inconsistent and poor
quality data.
We present streaming algorithms for computing commonly used aggregates on a
probabilistic stream. We present the first known, one pass streaming algorithm
for estimating the \AVG, improving results in \cite{JKV07}. We present the
first known streaming algorithms for estimating the number of \DISTINCT items
on probabilistic streams. Further, we present extensions to other aggregates
such as the repeat rate, quantiles, etc. In all cases, our algorithms work with
provable accuracy guarantees and within the space constraints of the data
stream model.Comment: 11 page