Related papers: Path Weights in Concentration Graphs
Causal graphs may inform covariate adjustment for estimating causal effects and improve estimation efficiency by exploiting the graphical structure. In many applications, however, the target causal parameter may not be point-identified due…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…
Deterministic variables are variables that are fully explained by one or more parent variables. They commonly arise when a variable has been algebraically constructed from one or more parent variables, as with composite variables, and in…
In order to take the weight of connection into consideration and to find a natural measurement of weight, we have collected papers in Econophysics and constructed a network of scientific communication to integrate idea transportation among…
Graph convolution (GConv) is a widely used technique that has been demonstrated to be extremely effective for graph learning applications, most notably node categorization. On the other hand, many GConv-based models do not quantify the…
Genetic interactions confer robustness on cells in response to genetic perturbations. This often occurs through molecular buffering mechanisms that can be predicted using, among other features, the degree of coexpression between genes,…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…
We consider a multi agent optimization problem where a set of agents collectively solves a global optimization problem with the objective function given by the sum of locally known convex functions. We focus on the case when information…
Urban mobility forecast and analysis can be addressed through grid-based and graph-based models. However, graph-based representations have the advantage of more realistically depicting the mobility networks and being more robust since they…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
Attention maps are a popular way of explaining the decisions of convolutional networks for image classification. Typically, for each image of interest, a single attention map is produced, which assigns weights to pixels based on their…
Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…
We analyze the weight diagram associated with foliations on the complex projective plane through the Hilbert-Mumford criterion in Geometric Invariant Theory, focusing in particular on invariants such as the algebraic multiplicity and the…
Much of the past work in network analysis has focused on analyzing discrete graphs, where binary edges represent the "presence" or "absence" of a relationship. Since traditional network measures (e.g., betweenness centrality) utilize a…
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of…
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are just the opposite of taking minors. We show that some classes…
Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…