33,062 research outputs found
Community detection for networks with unipartite and bipartite structure
Finding community structures in networks is important in network science,
technology, and applications. To date, most algorithms that aim to find
community structures only focus either on unipartite or bipartite networks. A
unipartite network consists of one set of nodes and a bipartite network
consists of two nonoverlapping sets of nodes with only links joining the nodes
in different sets. However, a third type of network exists, defined here as the
mixture network. Just like a bipartite network, a mixture network also consists
of two sets of nodes, but some nodes may simultaneously belong to two sets,
which breaks the nonoverlapping restriction of a bipartite network. The mixture
network can be considered as a general case, with unipartite and bipartite
networks viewed as its limiting cases. A mixture network can represent not only
all the unipartite and bipartite networks, but also a wide range of real-world
networks that cannot be properly represented as either unipartite or bipartite
networks in fields such as biology and social science. Based on this
observation, we first propose a probabilistic model that can find modules in
unipartite, bipartite, and mixture networks in a unified framework based on the
link community model for a unipartite undirected network [B Ball et al (2011
Phys. Rev. E 84 036103)]. We test our algorithm on synthetic networks (both
overlapping and nonoverlapping communities) and apply it to two real-world
networks: a southern women bipartite network and a human transcriptional
regulatory mixture network. The results suggest that our model performs well
for all three types of networks, is competitive with other algorithms for
unipartite or bipartite networks, and is applicable to real-world networks.Comment: 27 pages, 8 figures.
(http://iopscience.iop.org/1367-2630/16/9/093001
Marginal empirical likelihood and sure independence feature screening
We study a marginal empirical likelihood approach in scenarios when the
number of variables grows exponentially with the sample size. The marginal
empirical likelihood ratios as functions of the parameters of interest are
systematically examined, and we find that the marginal empirical likelihood
ratio evaluated at zero can be used to differentiate whether an explanatory
variable is contributing to a response variable or not. Based on this finding,
we propose a unified feature screening procedure for linear models and the
generalized linear models. Different from most existing feature screening
approaches that rely on the magnitudes of some marginal estimators to identify
true signals, the proposed screening approach is capable of further
incorporating the level of uncertainties of such estimators. Such a merit
inherits the self-studentization property of the empirical likelihood approach,
and extends the insights of existing feature screening methods. Moreover, we
show that our screening approach is less restrictive to distributional
assumptions, and can be conveniently adapted to be applied in a broad range of
scenarios such as models specified using general moment conditions. Our
theoretical results and extensive numerical examples by simulations and data
analysis demonstrate the merits of the marginal empirical likelihood approach.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1139 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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