相关论文: Learning Graphons via Structured Gromov-Wasserstei…

This paper considers learning of the graphical structure of a $p$-dimensional random vector $X \in R^p$ using both parametric and non-parametric methods. Unlike the previous works which observe $x$ directly, we consider the indirect…

Finding the mean of sampled data is a fundamental task in machine learning and statistics. However, in cases where the data samples are graph objects, defining a mean is an inherently difficult task. We propose a novel framework for…

Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal…

In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to…

Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or…

The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure spaces which has found broad applications in data science and machine learning. Driven by the need to analyze datasets whose objects have increasingly…

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…

Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit…

Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or…

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. Despite the significant gain in performance achieved via these…

In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…

A recent paper, ``A Graphon-Signal Analysis of Graph Neural Networks'', by Levie, analyzed message passing graph neural networks (MPNNs) by embedding the input space of MPNNs, i.e., attributed graphs (graph-signals), to a space of…

Recently, the theory of dense graph limits has received attention from multiple disciplines including graph theory, computer science, statistical physics, probability, statistics, and group theory. In this paper we initiate the study of the…

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…

Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due…

A sequence of graphs with diverging number of nodes is a dense graph sequence if the number of edges grows approximately as for complete graphs. To each such sequence a function, called graphon, can be associated, which contains information…

The graphon (W-graph), including the stochastic block model as a special case, has been widely used in modeling and analyzing network data. This random graph model is well-characterized by its graphon function, and estimation of the graphon…

Providing human-understandable insights into the inner workings of neural networks is an important step toward achieving more explainable and trustworthy AI. Existing approaches to such mechanistic interpretability typically require…

W-graph refers to a general class of random graph models that can be seen as a random graph limit. It is characterized by both its graphon function and its motif frequencies. In this paper, relying on an existing variational Bayes algorithm…

This paper focuses on the comparison of networks on the basis of statistical inference. For that purpose, we rely on smooth graphon models as a nonparametric modeling strategy that is able to capture complex structural patterns. The graphon…