Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: RFN: A Random-Feature Based Newton Method for Empirical Risk
  Minimization in Reproducing Kernel Hilbert Spaces   In supervised learning using kernel methods, we encounter a large-scale
finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Often
times large-scale finite-sum problems can be solved using efficient variants of
Newton's method where the Hessian is approximated via sub-samples. In RKHS,
however, the dependence of the penalty function to kernel makes standard
sub-sampling approaches inapplicable, since the gram matrix is not readily
available in a low-rank form. In this paper, we observe that for this class of
problems, one can naturally use kernel approximation to speed up the Newton's
method. Focusing on randomized features for kernel approximation, we provide a
novel second-order algorithm that enjoys local superlinear convergence and
global convergence in the high probability sense. The key to our analysis is
showing that the approximated Hessian via random features preserves the
spectrum of the original Hessian. We provide numerical experiments verifying
the efficiency of our approach, compared to variants of sub-sampling methods.

15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math