Estimating statistical aggregates on probabilistic data streams

The probabilistic-stream model was introduced by Jayram et al. [20]. 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 a potentially exponential number of classical "deterministic" streams where each item is deterministically one of the domain values. Designing efficient aggregation algorithms for probabilistic data is crucial for handling uncertainty in data-centric applications such as OLAP. Such algorithms are also useful in a variety of other setting including analyzing search engine traffic and aggregation in sensor networks. We present algorithms for computing commonly used aggregates on a probabilistic stream. We present the first one pass streaming algorithms for estimating the expected mean of a probabilistic stream, improving upon results in [20]. Next, we consider the problem of estimating frequency moments for probabilistic data. We propose a general approach to obtain unbiased estimators working over probabilistic data by utilizing unbiased estimators designed for standard streams. Applying this approach, we extend a classical data stream algorithm to obtain a one-pass algorithm for estimating F2, the second frequency moment. We present the first known streaming algorithms for estimating F0, the number of distinct items on probabilistic streams. Our work also gives an efficient one-pass algorithm for estimating the median of a probabilistic stream.