Related papers: One-connection rule for structural equation models
An arithmetical structure on a finite and connected graph G is a pair (d, r) of positive integer vectors such that r is primitive (the gcd of its entries is 1) and (diag(d) - A)r = 0, where A is the adjacency matrix of G. In this article,…
Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…
In semi-supervised learning on graphs, response variables observed at one node are used to estimate missing values at other nodes. The methods exploit correlations between nearby nodes in the graph. In this paper we prove that many such…
We give a necessary and sufficient graph-theoretic characterization of toric ideals of graphs that are unimodular. As a direct consequence, we provide the structure of unimodular graphs by proving that the incidence matrix of a graph $G$ is…
Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…
For a multivariate normal distribution, the sparsity of the covariance and precision matrices encodes complete information about independence and conditional independence properties. For general distributions, the covariance and precision…
Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…
Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks.…
Model-driven software engineering is a suitable method for dealing with the ever-increasing complexity of software development processes. Graphs and graph transformations have proven useful for representing such models and changes to them.…
A simple graph $G=(V,E)$ is a $(2,1)$-circuit if $|E|=2|V|$ and $|E(H)|\leq 2|V(H)|-1$ for every proper subgraph $H$ of $G$. Motivated, in part, by ongoing work to understand unique realisations of graphs on surfaces, we derive a…
The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However,…
This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…
It is proven that a connected graph is planar if and only if all its cocycles with at least four edges are "grounded" in the graph. The notion of grounding of this planarity criterion, which is purely combinatorial, stems from the intuitive…
The first part of the paper explains how to encode a one-cocycle and a two-cocycle on a group $G$ with values in its representation by networks of planar trivalent graphs with edges labelled by elements of $G$, elements of the…
Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse…
A colored Gaussian graphical model is a linear concentration model in which equalities among the concentrations are specified by a coloring of an underlying graph. Marigliano and Davies conjectured that every linear binomial that appears in…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several…
Functional causal models (fCMs) specify functional dependencies between random variables associated to the vertices of a graph. In directed acyclic graphs (DAGs), fCMs are well-understood: a unique probability distribution on the random…
Upon a matrix representation of a binary bipartite network, via the permutation invariance, a coupling geometry is computed to approximate the minimum energy macrostate of a network's system. Such a macrostate is supposed to constitute the…
Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data.…