29,790 research outputs found
Behavioral Communities and the Atomic Structure of Networks
We develop a theory of `behavioral communities' and the `atomic structure' of
networks. We define atoms to be groups of agents whose behaviors always match
each other in a set of coordination games played on the network. This provides
a microfoundation for a method of detecting communities in social and economic
networks. We provide theoretical results characterizing such behavior-based
communities and atomic structures and discussing their properties in large
random networks. We also provide an algorithm for identifying behavioral
communities. We discuss applications including: a method of estimating
underlying preferences by observing behavioral conventions in data, and
optimally seeding diffusion processes when there are peer interactions and
homophily. We illustrate the techniques with applications to high school
friendship networks and rural village networks
Optimal change point detection and localization in sparse dynamic networks
We study the problem of change point localization in dynamic networks models. We assume that we observe a sequence of independent adjacency matrices of the same size, each corresponding to a realization of an unknown inhomogeneous Bernoulli model. The underlying distribution of the adjacency matrices are piecewise constant, and may change over a subset of the time points, called change points. We are concerned with recovering the unknown number and positions of the change points. In our model setting, we allow for all the model parameters to change with the total number of time points, including the network size, the minimal spacing between consecutive change points, the magnitude of the smallest change and the degree of sparsity of the networks. We first identify a region of impossibility in the space of the model parameters such that no change point estimator is provably consistent if the data are generated according to parameters falling in that region. We propose a computationally-simple algorithm for network change point localization, called network binary segmentation, that relies on weighted averages of the adjacency matrices. We show that network binary segmentation is consistent over a range of the model parameters that nearly cover the complement of the impossibility region, thus demonstrating the existence of a phase transition for the problem at hand. Next, we devise a more sophisticated algorithm based on singular value thresholding, called local refinement, that delivers more accurate estimates of the change point locations. Under appropriate conditions, local refinement guarantees a minimax optimal rate for network change point localization while remaining computationally feasible
A semidefinite program for unbalanced multisection in the stochastic block model
We propose a semidefinite programming (SDP) algorithm for community detection
in the stochastic block model, a popular model for networks with latent
community structure. We prove that our algorithm achieves exact recovery of the
latent communities, up to the information-theoretic limits determined by Abbe
and Sandon (2015). Our result extends prior SDP approaches by allowing for many
communities of different sizes. By virtue of a semidefinite approach, our
algorithms succeed against a semirandom variant of the stochastic block model,
guaranteeing a form of robustness and generalization. We further explore how
semirandom models can lend insight into both the strengths and limitations of
SDPs in this setting.Comment: 29 page
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