Related papers: Probabilistic programming interfaces for random gr…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…
We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
We present GraphMoE, a novel neural network-based approach to learning generative models for random graphs. The neural network is trained to match the distribution of a class of random graphs by way of a moment estimator. The features used…
We study graphons as a non-parametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. Our algorithms and analysis go beyond previous work in several…
Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
The exploration of Graph Neural Networks (GNNs) for processing graph-structured data has expanded, particularly their potential for causal analysis due to their universal approximation capabilities. Anticipated to significantly enhance…
We investigate the problem of producing structured graph representations of visual scenes. Our work analyzes the role of motifs: regularly appearing substructures in scene graphs. We present new quantitative insights on such repeated…
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of…
Effectively combining logic reasoning and probabilistic inference has been a long-standing goal of machine learning: the former has the ability to generalize with small training data, while the latter provides a principled framework for…
Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
Graphons are general and powerful models for generating graphs of varying size. In this paper, we propose to directly model graphons using neural networks, obtaining Implicit Graphon Neural Representation (IGNR). Existing work in modeling…
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of…
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…
Recently, progress has been made towards improving relational reasoning in machine learning field. Among existing models, graph neural networks (GNNs) is one of the most effective approaches for multi-hop relational reasoning. In fact,…