Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: epsilon-Samples of Kernels   We study the worst case error of kernel density estimates via subset
approximation. A kernel density estimate of a distribution is the convolution
of that distribution with a fixed kernel (e.g. Gaussian kernel). Given a subset
(i.e. a point set) of the input distribution, we can compare the kernel density
estimates of the input distribution with that of the subset and bound the worst
case error. If the maximum error is eps, then this subset can be thought of as
an eps-sample (aka an eps-approximation) of the range space defined with the
input distribution as the ground set and the fixed kernel representing the
family of ranges. Interestingly, in this case the ranges are not binary, but
have a continuous range (for simplicity we focus on kernels with range of
[0,1]); these allow for smoother notions of range spaces.
  It turns out, the use of this smoother family of range spaces has an added
benefit of greatly decreasing the size required for eps-samples. For instance,
in the plane the size is O((1/eps^{4/3}) log^{2/3}(1/eps)) for disks (based on
VC-dimension arguments) but is only O((1/eps) sqrt{log (1/eps)}) for Gaussian
kernels and for kernels with bounded slope that only affect a bounded domain.
These bounds are accomplished by studying the discrepancy of these "kernel"
range spaces, and here the improvement in bounds are even more pronounced. In
the plane, we show the discrepancy is O(sqrt{log n}) for these kernels, whereas
for balls there is a lower bound of Omega(n^{1/4}).

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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg