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Probability Density Functions for Calculating Approximate Aggregates

Gramacki J., Gramacki A.

Foundations of Computing and Decision Sciences

2010

Vol. 35, No. 4

223-240

In the paper we show how one can use probability density function (PDF) for calculating approximate aggregates. The aggregates can be obtained very quickly and efficiently and there is no need to look through the large amount of data, as well as creating a sort of materialized aggregates (usually implemented as materialized views). Although the final results are only approximate, the method is extremely fast and can be successively used during initial phase of data exploration. We include simple experimental results which proof effectiveness of the method, especially if PDFs are typical, for example similar to Gaussian normal ones. If the PDFs differ from a normal distribution, one can consider making a proper preliminary transformation of the input variables or estimate PDFs by some nonparametric methods, for example using the so called kernel estimators. The later is used in the paper. To accelerate calculations, one can consider a usage of graphics processing unit (GPU). We point out this approach in the last section of the paper and give some preliminary results which are very promising.