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Distributed signal processing has attracted widespread attention in the scientific community due to its several advantages over centralized approaches. Recently, graph signal processing has risen to prominence, and adaptive distributed…
Generative models such as diffusion models have achieved remarkable success in state-of-the-art image and text tasks. Recently, score-based diffusion models have extended their success beyond image generation, showing competitive…
Recent years have witnessed a rise in real-world data captured with rich structural information that can be conveniently depicted by multi-relational graphs. While inference of continuous node features across a simple graph is rather…
For compressed sensing over arbitrarily connected networks, we consider the problem of estimating underlying sparse signals in a distributed manner. We introduce a new signal model that helps to describe inter-signal correlation among…
This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…
Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Hypergraphs are important objects to model ternary or higher-order relations of objects, and have a number of applications in analysing many complex datasets occurring in practice. In this work we study a new heat diffusion process in…
Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes follow an order. Graphs with ordered neighborhoods are a natural data representation for evolving graphs where…
While Graph Neural Networks (GNNs) have recently become the de facto standard for modeling relational data, they impose a strong assumption on the availability of the node or edge features of the graph. In many real-world applications,…
We consider a family of problems that are concerned about making predictions for the majority of unlabeled, graph-structured data samples based on a small proportion of labeled samples. Relational information among the data samples, often…
Text-conditioned image generation has made significant progress in recent years with generative adversarial networks and more recently, diffusion models. While diffusion models conditioned on text prompts have produced impressive and…
Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…
We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph…
Quantum graph neural networks offer a powerful paradigm for learning on graph-structured data, yet their explainability is complicated by measurement-induced stochasticity and the combinatorial nature of graph structure. In this paper, we…
Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…
Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous,…
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it…