19,070 research outputs found
Confidence sets for network structure
Latent variable models are frequently used to identify structure in
dichotomous network data, in part because they give rise to a Bernoulli product
likelihood that is both well understood and consistent with the notion of
exchangeable random graphs. In this article we propose conservative confidence
sets that hold with respect to these underlying Bernoulli parameters as a
function of any given partition of network nodes, enabling us to assess
estimates of 'residual' network structure, that is, structure that cannot be
explained by known covariates and thus cannot be easily verified by manual
inspection. We demonstrate the proposed methodology by analyzing student
friendship networks from the National Longitudinal Survey of Adolescent Health
that include race, gender, and school year as covariates. We employ a
stochastic expectation-maximization algorithm to fit a logistic regression
model that includes these explanatory variables as well as a latent stochastic
blockmodel component and additional node-specific effects. Although
maximum-likelihood estimates do not appear consistent in this context, we are
able to evaluate confidence sets as a function of different blockmodel
partitions, which enables us to qualitatively assess the significance of
estimated residual network structure relative to a baseline, which models
covariates but lacks block structure.Comment: 17 pages, 3 figures, 3 table
The interplay of microscopic and mesoscopic structure in complex networks
Not all nodes in a network are created equal. Differences and similarities
exist at both individual node and group levels. Disentangling single node from
group properties is crucial for network modeling and structural inference.
Based on unbiased generative probabilistic exponential random graph models and
employing distributive message passing techniques, we present an efficient
algorithm that allows one to separate the contributions of individual nodes and
groups of nodes to the network structure. This leads to improved detection
accuracy of latent class structure in real world data sets compared to models
that focus on group structure alone. Furthermore, the inclusion of hitherto
neglected group specific effects in models used to assess the statistical
significance of small subgraph (motif) distributions in networks may be
sufficient to explain most of the observed statistics. We show the predictive
power of such generative models in forecasting putative gene-disease
associations in the Online Mendelian Inheritance in Man (OMIM) database. The
approach is suitable for both directed and undirected uni-partite as well as
for bipartite networks
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