Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Rates of Sketched-regularized Algorithms for Least-Squares
  Regression over Hilbert Spaces   We investigate regularized algorithms combining with projection for
least-squares regression problem over a Hilbert space, covering nonparametric
regression over a reproducing kernel Hilbert space. We prove convergence
results with respect to variants of norms, under a capacity assumption on the
hypothesis space and a regularity condition on the target function. As a
result, we obtain optimal rates for regularized algorithms with randomized
sketches, provided that the sketch dimension is proportional to the effective
dimension up to a logarithmic factor. As a byproduct, we obtain similar results
for Nystr\"{o}m regularized algorithms. Our results are the first ones with
optimal, distribution-dependent rates that do not have any saturation effect
for sketched/Nystr\"{o}m regularized algorithms, considering both the
attainable and non-attainable cases.

21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th