Related papers: Fast Mixing in Sparse Random Ising Models
Social networks have a small number of large hubs, and a large number of small dense communities. We propose a generative model that captures both hub and dense structures. Based on recent results about graphons on line graphs, our model is…
We show that Glauber dynamics for $ p$-spin glass mixes exponentially slowly at inverse temperatures larger than a constant times $ \ln (p)/p $ for large enough $ p $. This is done by analyzing the energy landscape using Gaussian…
Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
Dynamic community detection concerns inferring how community memberships evolve over time, including the emergence, persistence, merging, and dissolution of groups in temporal networks. We propose a Bayesian nonparametric model for…
The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. Despite some breakthrough works in the mathematical understanding…
This article studies the estimation of latent community memberships from pairwise interactions in a network of $N$ nodes, where the observed interactions can be of arbitrary type, including binary, categorical, and vector-valued, and not…
We study Glauber dynamics for sampling from discrete distributions $\mu$ on the hypercube $\{\pm 1\}^n$. Recently, techniques based on spectral independence have successfully yielded optimal $O(n)$ relaxation times for a host of different…
Given a time-evolving network, how can we detect communities over periods of high internal and low external interactions? To address this question we generalize traditional local community detection in graphs to the setting of dynamic…
We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacency matrix nor its Laplacian concentrate around their…
Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random…
Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks…
We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising model on general graphs. We show that if \[(d-1)\tanh\beta<1,\] then there exists a constant C such that the discrete time mixing time of Gibbs…
Sparse prediction with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm for selection…
This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor.…
We consider the problem of sampling from the ferromagnetic Potts and random-cluster models on a general family of random graphs via the Glauber dynamics for the random-cluster model. The random-cluster model is parametrized by an edge…
We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world…
We study the coevolution of a generalized Glauber dynamics for Ising spins, with tunable threshold, and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of…
Trap models describe glassy dynamics as a stochastic process on a network of configurations representing local energy minima. We study within this class the paradigmatic Barrat-M\'ezard model, which has Glauber transition rates. Our focus…
As the availability and importance of temporal interaction data--such as email communication--increases, it becomes increasingly important to understand the underlying structure that underpins these interactions. Often these interactions…
We study the problem of learning the structure and parameters of the Ising model, a fundamental model of high-dimensional data, when observing the evolution of an associated Markov chain. A recent line of work has studied the natural…