Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Complexity of Learning with Kernels   A well-recognized limitation of kernel learning is the requirement to handle
a kernel matrix, whose size is quadratic in the number of training examples.
Many methods have been proposed to reduce this computational cost, mostly by
using a subset of the kernel matrix entries, or some form of low-rank matrix
approximation, or a random projection method. In this paper, we study lower
bounds on the error attainable by such methods as a function of the number of
entries observed in the kernel matrix or the rank of an approximate kernel
matrix. We show that there are kernel learning problems where no such method
will lead to non-trivial computational savings. Our results also quantify how
the problem difficulty depends on parameters such as the nature of the loss
function, the regularization parameter, the norm of the desired predictor, and
the kernel matrix rank. Our results also suggest cases where more efficient
kernel learning might be possible.

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The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: nlin