Related papers: Learning random points from geometric graphs or or…
Given a class $\mathcal G$ of graphs, let ${\mathcal G}_n$ denote the set of graphs in $\mathcal G$ on vertex set $[n]$. For certain classes $\mathcal G$, we are interested in the asymptotic behaviour of a random graph $R_n$ sampled…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural…
The unit ball random geometric graph $G=G^d_p(\lambda,n)$ has as its vertices $n$ points distributed independently and uniformly in the $d$-dimensional unit ball, with two vertices adjacent if and only if their $l_p$-distance is at most…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…
Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…
There has been growing interest in studies of general random intersection graphs. In this paper, we consider a general random intersection graph $\mathbb{G}(n,\overrightarrow{a}, \overrightarrow{K_n},P_n)$ defined on a set $\mathcal{V}_n$…
We study the problem of learning a hidden hypergraph $G=(V,E)$ by making a single batch of queries (non-adaptively). We consider the hyperedge detection model, in which every query must be of the form: ``Does this set $S\subseteq V$ contain…
A graph is called (generically) rigid in $\mathbb{R}^d$ if, for any choice of sufficiently generic edge lengths, it can be embedded in $\mathbb{R}^d$ in a finite number of distinct ways, modulo rigid transformations. Here we deal with the…
We study the problem of learning a hypergraph via edge detecting queries. In this problem, a learner queries subsets of vertices of a hidden hypergraph and observes whether these subsets contain an edge or not. In general, learning a…
We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are particularly prevalent in random geometric graphs and appear in the Laplacian and adjacency…
Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…
We demonstrate that frequently appearing objects can be discovered by training randomly sampled patches from a small number of images (100 to 200) by self-supervision. Key to this approach is the pattern space, a latent space of patterns…
In the random geometric graph model $\mathsf{Geo}_d(n,p)$, we identify each of our $n$ vertices with an independently and uniformly sampled vector from the $d$-dimensional unit sphere, and we connect pairs of vertices whose vectors are…
Representing words by vectors, or embeddings, enables computational reasoning and is foundational to automating natural language tasks. For example, if word embeddings of similar words contain similar values, word similarity can be readily…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
One-dimensional geometric random graphs are constructed by distributing $n$ nodes uniformly and independently on a unit interval and then assigning an undirected edge between any two nodes that have a distance at most $r_n$. These graphs…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Uncover the vertices of a given graph, deterministic or random, in random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization…