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Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
The rapid growth of graph data poses significant challenges in storage, transmission, and particularly the training of graph neural networks (GNNs). To address these challenges, graph condensation (GC) has emerged as an innovative solution.…
Graph learning is the fundamental task of estimating unknown graph connectivity from available data. Typical approaches assume that not only is all information available simultaneously but also that all nodes can be observed. However, in…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
This paper examines the maximum code rate achievable by a data-driven communication system over some unknown discrete memoryless channel in the finite blocklength regime. A class of channel codes, called learning-based channel codes, is…
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish…
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…
This article characterizes new boundary points on the capacity region of certain classes of more capable broadcast channels (BC) with uni-directional cooperation from the stronger to the weaker receiver. The new boundary points are achieved…
Flat-fading channels that are correlated in time are considered under peak and average power constraints. For discrete-time channels, a new upper bound on the capacity per unit time is derived. A low SNR analysis of a full-scattering vector…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…
This work establishes novel optimum mixing bounds for the Glauber dynamics on the Hard-core and Ising models. These bounds are expressed in terms of the local connective constant of the underlying graph $G$. This is a notion of effective…
Graph Neural Networks (GNNs) achieve state-of-the-art performance in various graph-related tasks. However, the black-box nature often limits their interpretability and trustworthiness. Numerous explainability methods have been proposed to…
We consider the class of conditional graph patterns (\emph{CGPs}) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider…
In this work, we study two models of arbitrarily varying channels, when causal side information is available at the encoder in a causal manner. First, we study the arbitrarily varying channel (AVC) with input and state constraints, when the…
This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
We consider a point-to-point communication system, where in addition to the encoder and the decoder, there is a helper that observes non-causally the realization of the noise vector and provides a (lossy) rate-$R_{\mbox{\tiny h}}$…
In this paper, we consider different aspects of the network functional compression problem where computation of a function (or, some functions) of sources located at certain nodes in a network is desired at receiver(s). The rate region of…
Over the last few years, we have witnessed the availability of an increasing data generated from non-Euclidean domains, which are usually represented as graphs with complex relationships, and Graph Neural Networks (GNN) have gained a high…