Related papers: Parameterizing Network Graph Heterogeneity using a…
Diffusion models based on permutation-equivariant networks can learn permutation-invariant distributions for graph data. However, in comparison to their non-invariant counterparts, we have found that these invariant models encounter greater…
Generating graphs that preserve characteristic structures while promoting sample diversity can be challenging, especially when the number of graph observations is small. Here, we tackle the problem of graph generation from only one observed…
Real-world networks, like social networks or the internet infrastructure, have structural properties such as large clustering coefficients that can best be described in terms of an underlying geometry. This is why the focus of the…
A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice of wavelet for a dataset of graphs, such that their…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…
Consider a random graph $G$ of size $N$ constructed according to a \textit{graphon} $w \, : \, [0,1]^{2} \mapsto [0,1]$ as follows. First embed $N$ vertices $V = \{v_1, v_2, \ldots, v_N\}$ into the interval $[0,1]$, then for each $i < j$…
In this work, we revisit the estimation of the model parameters of a Weibull distribution based on iid observations, using the maximum likelihood estimation (MLE) method which does not yield closed expressions of the estimators. Among other…
Diffusion models achieve state-of-the-art performance in generating realistic objects and have been successfully applied to images, text, and videos. Recent work has shown that diffusion can also be defined on graphs, including graph…
Most real-world networks are noisy and incomplete samples from an unknown target distribution. Refining them by correcting corruptions or inferring unobserved regions typically improves downstream performance. Inspired by the impressive…
We study the problem of parameter estimation based on infection data from an epidemic outbreak on a graph. We assume that successive infections occur via contagion; i.e., transmissions can only spread across existing directed edges in the…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
I propose an estimation algorithm for Exponential Random Graph Models (ERGM), a popular statistical network model for estimating the structural parameters of strategic network formation in economics and finance. Existing methods often…
Graph generation is an important area in network science. Traditional approaches focus on replicating specific properties of real-world graphs, such as small diameters or power-law degree distributions. Recent advancements in deep learning,…
Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task…
In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…
We consider high-dimensional distribution estimation through autoregressive networks. By combining the concepts of sparsity, mixtures and parameter sharing we obtain a simple model which is fast to train and which achieves state-of-the-art…
This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables…
The degree distribution is one of the most fundamental graph properties of interest for real-world graphs. It has been widely observed in numerous domains that graphs typically have a tailed or scale-free degree distribution. While the…
Exchangeability is a desired statistical property of network ensembles requiring their invariance upon relabelling of the nodes. However combining sparsity of network ensembles with exchangeability is challenging. Here we propose a…