Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-Dimensional Graphical Model Selection Using $\ell_1$-Regularized
  Logistic Regression   We consider the problem of estimating the graph structure associated with a
discrete Markov random field. We describe a method based on
$\ell_1$-regularized logistic regression, in which the neighborhood of any
given node is estimated by performing logistic regression subject to an
$\ell_1$-constraint. Our framework applies to the high-dimensional setting, in
which both the number of nodes $p$ and maximum neighborhood sizes $d$ are
allowed to grow as a function of the number of observations $n$. Our main
results provide sufficient conditions on the triple $(n, p, d)$ for the method
to succeed in consistently estimating the neighborhood of every node in the
graph simultaneously. Under certain assumptions on the population Fisher
information matrix, we prove that consistent neighborhood selection can be
obtained for sample sizes $n = \Omega(d^3 \log p)$, with the error decaying as
$\order(\exp(-C n/d^3))$ for some constant $C$. If these same assumptions are
imposed directly on the sample matrices, we show that $n = \Omega(d^2 \log p)$
samples are sufficient.

21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg