Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sampling Sketches for Concave Sublinear Functions of Frequencies   We consider massive distributed datasets that consist of elements modeled as
key-value pairs and the task of computing statistics or aggregates where the
contribution of each key is weighted by a function of its frequency (sum of
values of its elements). This fundamental problem has a wealth of applications
in data analytics and machine learning, in particular, with concave sublinear
functions of the frequencies that mitigate the disproportionate effect of keys
with high frequency. The family of concave sublinear functions includes low
frequency moments ($p \leq 1$), capping, logarithms, and their compositions. A
common approach is to sample keys, ideally, proportionally to their
contributions and estimate statistics from the sample. A simple but costly way
to do this is by aggregating the data to produce a table of keys and their
frequencies, apply our function to the frequency values, and then apply a
weighted sampling scheme. Our main contribution is the design of composable
sampling sketches that can be tailored to any concave sublinear function of the
frequencies. Our sketch structure size is very close to the desired sample size
and our samples provide statistical guarantees on the estimation quality that
are very close to that of an ideal sample of the same size computed over
aggregated data. Finally, we demonstrate experimentally the simplicity and
effectiveness of our methods.

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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn