Related papers: Graphical modeling of stochastic processes driven …

The exploration of Graph Neural Networks (GNNs) for processing graph-structured data has expanded, particularly their potential for causal analysis due to their universal approximation capabilities. Anticipated to significantly enhance…

Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs…

Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…

Markov networks and Bayesian networks are effective graphic representations of the dependencies embedded in probabilistic models. It is well known that independencies captured by Markov networks (called graph-isomorphs) have a finite…

We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph…

This paper formalizes connections between stability of polynomials and convergence rates of Markov Chain Monte Carlo (MCMC) algorithms. We prove that if a (multivariate) partition function is nonzero in a region around a real point…

Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of…

We give a construction for a self-test for any connected graph state. In other words, for each connected graph state we give a set of non-local correlations that can only be achieved (quantumly) by that particular graph state and certain…

We study a class of stationary Markov processes with marginal distributions identifiable by moments such that every conditional moment of degree say $m$ is a polynomial of degree at most $m\;\text{.}\;$ We show that then under some…

This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The…

We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…

In this paper we discuss four problems regarding Markov equivalences for subclasses of loopless mixed graphs. We classify these four problems as finding conditions for internal Markov equivalence, which is Markov equivalence within a…

This work proposes a novel distributed framework for verifying the incremental stability of large-scale systems with unknown dynamics and known interconnection structures using graph neural networks. Our proposed approach relies on the…

The $\mathrm{Caus}[-]$ construction takes a base category of ``raw materials'' and builds a category of higher order causal processes, that is a category whose types encode causal (a.k.a. signalling) constraints between collections of…

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…

Graph states are well-entangled quantum states that are defined based on a graph. Of course, if two graphs are isomorphic their associated states are the same. Also, we know local operations do not change the entanglement of quantum states.…

An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…

The linear Lyapunov equation of a covariance matrix parametrizes the equilibrium covariance matrix of a stochastic process. This parametrization can be interpreted as a new graphical model class, and we show how the model class behaves…

We use the concept of a Kirchhoff resistor network (alternatively random walk on a network) to probe connected graphs and produce symmetry revealing canonical labelings of the graph(s) nodes and edges.

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify…