Related papers: A survey on graphs with convex quadratic stability…
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…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
The stability number of a graph G, denoted by alpha(G), is the cardinality of a maximum stable set, and mu(G) is the cardinality of a maximum matching in G. If alpha(G) + mu(G) equals its order, then G is a Koenig-Egervary graph. We call G…
We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex.…
The slope number of a graph $G$ is the smallest number of slopes needed for the segments representing the edges in any straight-line drawing of $G$. It serves as a measure of the visual complexity of a graph drawing. Several bounds on the…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
When approaching graph signal processing tasks, graphs are usually assumed to be perfectly known. However, in many practical applications, the observed (inferred) network is prone to perturbations which, if ignored, will hinder performance.…
The chromatic vertex (resp.\ edge) stability number ${\rm vs}_{\chi}(G)$ (resp.\ ${\rm es}_{\chi}(G)$) of a graph $G$ is the minimum number of vertices (resp.\ edges) whose deletion results in a graph $H$ with $\chi(H)=\chi(G)-1$. In the…
Recently, the stability of graph filters has been studied as one of the key theoretical properties driving the highly successful graph convolutional neural networks (GCNs). The stability of a graph filter characterizes the effect of…
Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…
The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging…
In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable…
Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…
In this paper, we study the stability result of a well-known theorem of Bondy. We prove that for any 2-connected non-hamiltonian graph, if every vertex except for at most one vertex has degree at least $k$, then it contains a cycle of…
In the problem of structured prediction with graph representation learning (GRL for short), the hypothesis returned by the algorithm maps the set of features in the \emph{receptive field} of the targeted vertex to its label. To understand…