Related papers: Dense multigraphon-valued stochastic processes and…

This paper considers the discrete-time version of Altafini's model for opinion dynamics in which the interaction among a group of agents is described by a time-varying signed digraph. Prompted by an idea from [1], exponential convergence of…

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…

Recently, van der Hofstad, Komj\'{a}thy, and Vadon (2022) identified the critical point for the emergence of a giant connected component for the bipartite configuration model (BCM) and used this to analyze its associated random intersection…

This paper proposes a novel analysis for the Scaffold algorithm, a popular method for dealing with data heterogeneity in federated learning. While its convergence in deterministic settings--where local control variates mitigate client…

This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…

We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…

Representation learning over graph structure data has been widely studied due to its wide application prospects. However, previous methods mainly focus on static graphs while many real-world graphs evolve over time. Modeling such evolution…

We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…

Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop…

Using the weak convergence approach to large deviations, we formulate and prove the large deviation principle (LDP) for W-random graphs in the cut-norm topology. This generalizes the LDP for Erd\H{o}s-R{\' e}nyi random graphs by Chatterjee…

A significant generalization of the Erd\"os-R\'enyi random graph model is an `inhomogeneous' random graph where the edge probabilities vary according to vertex types. We identify the threshold value for this random graph with a finite…

A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…

High-dimensional networks play a key role in understanding complex relationships. These relationships are often dynamic in nature and can change with multiple external factors (e.g., time and groups). Methods for estimating graphical models…

In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…

Deep Learning has made a great progress for these years. However, it is still difficult to master the implement of various models because different researchers may release their code based on different frameworks or interfaces. In this…

Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…

In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is…

We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…

Diffusion models, which leverage stochastic processes to capture complex data distributions effectively, have shown their performance as generative models, achieving notable success in image-related tasks through iterative denoising…

Modern approaches for learning on dynamic graphs have adopted the use of batches instead of applying updates one by one. The use of batches allows these techniques to become helpful in streaming scenarios where updates to graphs are…