Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation and learning by greedy algorithms   We consider the problem of approximating a given element $f$ from a Hilbert
space $\mathcal{H}$ by means of greedy algorithms and the application of such
procedures to the regression problem in statistical learning theory. We improve
on the existing theory of convergence rates for both the orthogonal greedy
algorithm and the relaxed greedy algorithm, as well as for the forward stepwise
projection algorithm. For all these algorithms, we prove convergence results
for a variety of function classes and not simply those that are related to the
convex hull of the dictionary. We then show how these bounds for convergence
rates lead to a new theory for the performance of greedy algorithms in
learning. In particular, we build upon the results in [IEEE Trans. Inform.
Theory 42 (1996) 2118--2132] to construct learning algorithms based on greedy
approximations which are universally consistent and provide provable
convergence rates for large classes of functions. The use of greedy algorithms
in the context of learning is very appealing since it greatly reduces the
computational burden when compared with standard model selection using general
dictionaries.

11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph