The management of uncertain, probabilistic data has recently emerged as a useful paradigm for dealing with the inherent unreliabilities of several real-world application domains, including data cleaning, information integration, and pervasive, multi-sensor computing. Unlike conventional data sets, a set of probabilistic tuples defines a probability distribution over an exponential number of possible worlds (i.e., grounded, deterministic databases). This possible worlds interpretation allows for clean query semantics but also raises hard computational problems for probabilistic database query processors. To further complicate matters, in many scenarios (e.g., large-scale process and environmental monitoring using multiple sensor modalities), probabilistic data tuples arrive and need to be processed in a streaming fashion; that is, using limited memory and CPU resources and without the benefit of multiple passes over a static probabilistic database. Such probabilistic data streams raise a host of new research challenges for stream-processing engines that, to date, remain largely unaddressed.
In this paper, we propose the first space- and time-efficient algorithms for approximating complex aggregate queries (including, the number of distinct values and join/self-join sizes) over probabilistic data streams. Following the possible-worlds semantics, such aggregates essentially define probability distributions over the space of possible aggregation results, and our goal is to characterize such distributions through efficient approximations of their key moments (such as expectation and variance). Our algorithms offer strong randomized estimation guarantees while using only sublinear space in the size of the stream(s), and rely on novel, concise streaming sketch synopses that extend conventional sketching ideas to the probabilistic streams setting. Our experimental results verify the effectiveness of our approach.
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