Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical mechanics of sparse generalization and model selection   One of the crucial tasks in many inference problems is the extraction of
sparse information out of a given number of high-dimensional measurements. In
machine learning, this is frequently achieved using, as a penality term, the
$L_p$ norm of the model parameters, with $p\leq 1$ for efficient dilution. Here
we propose a statistical-mechanics analysis of the problem in the setting of
perceptron memorization and generalization. Using a replica approach, we are
able to evaluate the relative performance of naive dilution (obtained by
learning without dilution, following by applying a threshold to the model
parameters), $L_1$ dilution (which is frequently used in convex optimization)
and $L_0$ dilution (which is optimal but computationally hard to implement).
Whereas both $L_p$ diluted approaches clearly outperform the naive approach, we
find a small region where $L_0$ works almost perfectly and strongly outperforms
the simpler to implement $L_1$ dilution.

19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph