87 research outputs found
Testing goodness-of-fit of random graph models
Random graphs are matrices with independent 0, 1 elements with probabilities
determined by a small number of parameters. One of the oldest model is the
Rasch model where the odds are ratios of positive numbers scaling the rows and
columns. Later Persi Diaconis with his coworkers rediscovered the model for
symmetric matrices and called the model beta. Here we give goodnes-of-fit tests
for the model and extend the model to a version of the block model introduced
by Holland, Laskey, and Leinhard
A modularity based spectral method for simultaneous community and anti-community detection
In a graph or complex network, communities and anti-communities are node sets
whose modularity attains extremely large values, positive and negative,
respectively. We consider the simultaneous detection of communities and
anti-communities, by looking at spectral methods based on various matrix-based
definitions of the modularity of a vertex set. Invariant subspaces associated
to extreme eigenvalues of these matrices provide indications on the presence of
both kinds of modular structure in the network. The localization of the
relevant invariant subspaces can be estimated by looking at particular matrix
angles based on Frobenius inner products
A Generic Sample Splitting Approach for Refined Community Recovery in Stochastic Block Models
We propose and analyze a generic method for community recovery in stochastic
block models and degree corrected block models. This approach can exactly
recover the hidden communities with high probability when the expected node
degrees are of order or higher. Starting from a roughly correct
community partition given by some conventional community recovery algorithm,
this method refines the partition in a cross clustering step. Our results
simplify and extend some of the previous work on exact community recovery,
discovering the key role played by sample splitting. The proposed method is
simple and can be implemented with many practical community recovery
algorithms.Comment: 19 page
Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels
Variational methods for parameter estimation are an active research area,
potentially offering computationally tractable heuristics with theoretical
performance bounds. We build on recent work that applies such methods to
network data, and establish asymptotic normality rates for parameter estimates
of stochastic blockmodel data, by either maximum likelihood or variational
estimation. The result also applies to various sub-models of the stochastic
blockmodel found in the literature.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1124 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs
Graph neural networks (GNNs) have been widely used in various graph-related
problems such as node classification and graph classification, where the
superior performance is mainly established when natural node features are
available. However, it is not well understood how GNNs work without natural
node features, especially regarding the various ways to construct artificial
ones. In this paper, we point out the two types of artificial node
features,i.e., positional and structural node features, and provide insights on
why each of them is more appropriate for certain tasks,i.e., positional node
classification, structural node classification, and graph classification.
Extensive experimental results on 10 benchmark datasets validate our insights,
thus leading to a practical guideline on the choices between different
artificial node features for GNNs on non-attributed graphs. The code is
available at https://github.com/zjzijielu/gnn-exp/.Comment: This paper has been accepted to the Sixth International Workshop on
Deep Learning on Graphs (DLG-KDD'21) (co-located with KDD'21
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