Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal classification in sparse Gaussian graphic model   Consider a two-class classification problem where the number of features is
much larger than the sample size. The features are masked by Gaussian noise
with mean zero and covariance matrix $\Sigma$, where the precision matrix
$\Omega=\Sigma^{-1}$ is unknown but is presumably sparse. The useful features,
also unknown, are sparse and each contributes weakly (i.e., rare and weak) to
the classification decision. By obtaining a reasonably good estimate of
$\Omega$, we formulate the setting as a linear regression model. We propose a
two-stage classification method where we first select features by the method of
Innovated Thresholding (IT), and then use the retained features and Fisher's
LDA for classification. In this approach, a crucial problem is how to set the
threshold of IT. We approach this problem by adapting the recent innovation of
Higher Criticism Thresholding (HCT). We find that when useful features are rare
and weak, the limiting behavior of HCT is essentially just as good as the
limiting behavior of ideal threshold, the threshold one would choose if the
underlying distribution of the signals is known (if only). Somewhat
surprisingly, when $\Omega$ is sufficiently sparse, its off-diagonal
coordinates usually do not have a major influence over the classification
decision. Compared to recent work in the case where $\Omega$ is the identity
matrix [Proc. Natl. Acad. Sci. USA 105 (2008) 14790-14795; Philos. Trans. R.
Soc. Lond. Ser. A Math. Phys. Eng. Sci. 367 (2009) 4449-4470], the current
setting is much more general, which needs a new approach and much more
sophisticated analysis. One key component of the analysis is the intimate
relationship between HCT and Fisher's separation. Another key component is the
tight large-deviation bounds for empirical processes for data with
unconventional correlation structures, where graph theory on vertex coloring
plays an important role.

25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys