Related papers: On decomposable random graphs
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…
A parametrization of hypergraphs based on the geometry of points in $\mathbf{R}^d$ is developed. Informative prior distributions on hypergraphs are induced through this parametrization by priors on point configurations via spatial…
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
We introduce the Contextual Graph Markov Model, an approach combining ideas from generative models and neural networks for the processing of graph data. It founds on a constructive methodology to build a deep architecture comprising layers…
We characterize the reachability probabilities in stochastic directed graphs by means of reinforcement learning methods. In particular, we show that the dynamics of the transition probabilities in a stochastic digraph can be modeled via a…
Dynamical processes, such as the diffusion of knowledge, opinions, pathogens, "fake news", innovation, and others, are highly dependent on the structure of the social network on which they occur. However, questions on why most social…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…
We study the free product of rooted graphs and its various decompositions using quantum probabilistic methods. We show that the free product of rooted graphs is canonically associated with free independence, which completes the proof of the…
Sidorenko's Conjecture asserts that every bipartite graph H has the Sidorenko property, i.e., a quasirandom graph minimizes the density of H among all graphs with the same edge density. We study a stronger property, which requires that a…
We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…
This work reports the most relevant technical aspects in the problem of learning the \emph{Markov network structure} from data. Such problem has become increasingly important in machine learning, and many other application fields of machine…
Global Markov properties in mixed graphs are usually formulated in terms of the path-oriented m-separation or by use of augmented graphs (similar to moral graphs in the case of directed acyclic graphs). We provide an alternative…
We describe the implementation of the Giudici-Green Metropolis sampling method for decomposable graphs using a variety of structures to represent the graph. These comprise the graph itself, the Junction tree, the Almond tree and the Ibarra…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…