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In this work we develop a theory of hierarchical clustering for graphs. Our modeling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons…
The latent stochastic block model is a flexible and widely used statistical model for the analysis of network data. Extensions of this model to a dynamic context often fail to capture the persistence of edges in contiguous network…
The present work continues the program of summing planar Feynman graphs on the world sheet. Although it is based on the same classical action introduced in the earlier work, there are important new features: Instead of the path integral…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…
We develop a systematic procedure to quantise canonically Hamiltonians of light-matter models of transmission lines coupled through lumped linear lossless ideal nonreciprocal elements, that break time-reversal symmetry, in a circuit QED…
We study conditions under which a given hypergraph is randomly robust Hamiltonian, which means that a random sparsification of the host graph contains a Hamilton cycle with high probability. Our main contribution provides nearly optimal…
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…
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…
Graph clustering is a central topic in unsupervised learning with a multitude of practical applications. In recent years, multi-view graph clustering has gained a lot of attention for its applicability to real-world instances where one has…
Convolutional neural networks (CNNs) have achieved superior accuracy in many visual related tasks. However, the inference process through intermediate layers is opaque, making it difficult to interpret such networks or develop trust in…
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…
Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language…
The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase…
Many empirical networks are intrinsically polyadic, with interactions occurring within groups of agents of arbitrary size. There are, however, few flexible null models that can support statistical inference for such polyadic networks. We…
Graph clustering is widely used in many data analysis applications. In this paper we propose several parallel graph clustering algorithms based on Monte Carlo simulations and expectation maximization in the context of stochastic block…
Many real networks can be understood as two complementary networks with two kind of nodes. This is the case of metabolic networks where the first network has chemical compounds as nodes and the second one has nodes as reactions. The second…
The paper exposes a non-parametric approach to latent and co-latent modeling of bivariate data, based upon alternating minimization of the Kullback-Leibler divergence (EM algorithm) for complete log-linear models. For categorical data, the…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…
Community detection in graphs is a problem that is likely to be relevant whenever network data appears, and consequently the problem has received much attention with many different methods and algorithms applied. However, many of these…