相关论文: Statistical inference on random dot product graphs…
With the emergence of dynamic multiplex networks, corresponding to graphs where multiple types of edges evolve over time, a key inferential task is to determine whether the layers associated with different edge types differ in their…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
Graph states are fundamental objects in the theory of quantum information due to their simple classical description and rich entanglement structure. They are also intimately related to IQP circuits, which have applications in quantum…
Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal…
In this work, we study the spectrum of the regularized normalized Laplacian for random geometric graphs (RGGs) in both the connectivity and thermodynamic regimes. We prove that the limiting eigenvalue distribution (LED) of the normalized…
Respondent-driven sampling (RDS) is a chain-referral method for sampling members of a hidden or hard-to-reach population such as sex workers, homeless people, or drug users via their social network. Most methodological work on RDS has…
Let $G_n$ be a random geometric graph with vertex set $[n]$ based on $n$ i.i.d.\ random vectors $X_1,\ldots,X_n$ drawn from an unknown density $f$ on $\R^d$. An edge $(i,j)$ is present when $\|X_i -X_j\| \le r_n$, for a given threshold…
In this article, we analyze the limiting eigenvalue distribution (LED) of random geometric graphs (RGGs). The RGG is constructed by uniformly distributing $n$ nodes on the $d$-dimensional torus $\mathbb{T}^d \equiv [0, 1]^d$ and connecting…
Connectivity of wireless sensor networks (WSNs) is a fundamental global property expected to be maintained even though some sensor nodes are at fault. In this paper, we investigate the connectivity of random geometric graphs (RGGs) in the…
A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the $d$-dimensional Euclidean space with $d\geq 2$. Spheres arrive sequentially at…
Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Starting with a collection of traces generated by process executions, process discovery is the task of constructing a simple model that describes the process, where simplicity is often measured in terms of model size. The challenge of…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…
Learning distributions of graphs can be used for automatic drug discovery, molecular design, complex network analysis, and much more. We present an improved framework for learning generative models of graphs based on the idea of deep state…
Denoising Diffusion Probabilistic Models (DDPMs) represent a contemporary class of generative models with exceptional qualities in both synthesis and maximizing the data likelihood. These models work by traversing a forward Markov Chain…
The distribution $\mathsf{RGG}(n,\mathbb{S}^{d-1},p)$ is formed by sampling independent vectors $\{V_i\}_{i = 1}^n$ uniformly on $\mathbb{S}^{d-1}$ and placing an edge between pairs of vertices $i$ and $j$ for which $\langle V_i,V_j\rangle…