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Much research has been devoted to the efficient computation of relational aggregations and, specifically, the efficient execution of the datacube operation. In this paper, we consider the inverse problem, that of deriving (approximately) the original data from the aggregates. We motivate this problem in the context of two specific application areas, approximate query answering and data analysis. We propose a framework based on the notion of information entropy that enables us to estimate the original values in a data set, given only aggregated information about it. We then show how approximate queries on the data from which the aggregates were derived can be performed using our framework. We also describe an alternate use of the proposed framework that enables us to identify values that deviate from the underlying data distribution, suitable for data mining purposes. We present a detailed performance study of the algorithms using both real and synthetic data, highlighting the benefits of our approach as well as the efficiency of the proposed solutions. Finally, we evaluate our techniques with a case study on a real data set, which illustrates the applicability of our approach.
Index Terms- Data warehouse, datacube, approximate query answering, deviation detection.

T. Palpanas, N. Koudas and A. Mendelzon, "Using Datacube Aggregates for Approximate Querying and Deviation Detection," in IEEE Transactions on Knowledge & Data Engineering, vol. 17, no. , pp. 1465-1477, 2005.
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