Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparse Logistic Regression Learns All Discrete Pairwise Graphical Models   We characterize the effectiveness of a classical algorithm for recovering the
Markov graph of a general discrete pairwise graphical model from i.i.d.
samples. The algorithm is (appropriately regularized) maximum conditional
log-likelihood, which involves solving a convex program for each node; for
Ising models this is $\ell_1$-constrained logistic regression, while for more
general alphabets an $\ell_{2,1}$ group-norm constraint needs to be used. We
show that this algorithm can recover any arbitrary discrete pairwise graphical
model, and also characterize its sample complexity as a function of model
width, alphabet size, edge parameter accuracy, and the number of variables. We
show that along every one of these axes, it matches or improves on all existing
results and algorithms for this problem. Our analysis applies a sharp
generalization error bound for logistic regression when the weight vector has
an $\ell_1$ constraint (or $\ell_{2,1}$ constraint) and the sample vector has
an $\ell_{\infty}$ constraint (or $\ell_{2, \infty}$ constraint). We also show
that the proposed convex programs can be efficiently solved in $\tilde{O}(n^2)$
running time (where $n$ is the number of variables) under the same statistical
guarantees. We provide experimental results to support our analysis.

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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol