2,567 research outputs found
A Consistent Histogram Estimator for Exchangeable Graph Models
Exchangeable graph models (ExGM) subsume a number of popular network models.
The mathematical object that characterizes an ExGM is termed a graphon. Finding
scalable estimators of graphons, provably consistent, remains an open issue. In
this paper, we propose a histogram estimator of a graphon that is provably
consistent and numerically efficient. The proposed estimator is based on a
sorting-and-smoothing (SAS) algorithm, which first sorts the empirical degree
of a graph, then smooths the sorted graph using total variation minimization.
The consistency of the SAS algorithm is proved by leveraging sparsity concepts
from compressed sensing.Comment: 28 pages, 5 figure
Stochastic blockmodel approximation of a graphon: Theory and consistent estimation
Non-parametric approaches for analyzing network data based on exchangeable
graph models (ExGM) have recently gained interest. The key object that defines
an ExGM is often referred to as a graphon. This non-parametric perspective on
network modeling poses challenging questions on how to make inference on the
graphon underlying observed network data. In this paper, we propose a
computationally efficient procedure to estimate a graphon from a set of
observed networks generated from it. This procedure is based on a stochastic
blockmodel approximation (SBA) of the graphon. We show that, by approximating
the graphon with a stochastic block model, the graphon can be consistently
estimated, that is, the estimation error vanishes as the size of the graph
approaches infinity.Comment: 20 pages, 4 figures, 2 algorithms. Neural Information Processing
Systems (NIPS), 201
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