We consider the data stream model where an n-dimensional vector x is updated coordinate-wise by a stream of updates. The frequency estimation problem is to process the stream in a single pass and using small memory such that an estimate for xi for any i can be retrieved. We present the first algorithms for ℓ2-based frequency estimation that exhibit a tradeoff between the precision (additive error) of its estimate and the confidence on that estimate, for a range of parameter values. We show that our algorithms are optimal for a range of parameters for the class of matrix algorithms, namely, those whose state corresponding to a vector x can be represented as Ax for some m x n matrix A. All known algorithms for ℓ2-based frequency estimation are matrix algorithms. © Springer-Verlag 2012.
CITATION STYLE
Ganguly, S. (2012). Precision vs confidence tradeoffs for ℓ2-based frequency estimation in data streams. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7676 LNCS, pp. 64–74). Springer Verlag. https://doi.org/10.1007/978-3-642-35261-4_10
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