Related papers: On statistical learning of graphs
We present an interactive framework that, given a membership test for a graph class $\mathcal{G}$ and a number $k$, finds and tests unavoidable sets for the class of graphs in $\mathcal{G}$ of path-width at most $k$. We put special emphasis…
Despite recent success in using the invariance principle for out-of-distribution (OOD) generalization on Euclidean data (e.g., images), studies on graph data are still limited. Different from images, the complex nature of graphs poses…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
The Surjective Homomorphism problem is to test whether a given graph G called the guest graph allows a vertex-surjective homomorphism to some other given graph H called the host graph. The bijective and injective homomorphism problems can…
The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…
Inspired by Franks' classification of irreducible shifts of finite type we provide a short list of allowed moves on graphs that preserves the stable isomorphism class of the associated C*-algebras. We show that if two graphs have stably…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…
Graph neural networks are prominent models for representation learning over graphs, where the idea is to iteratively compute representations of nodes of an input graph through a series of transformations in such a way that the learned graph…
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models,…
Computational efficiency is a major bottleneck in using classic graph-based approaches for semi-supervised learning on datasets with a large number of unlabeled examples. Known techniques to improve efficiency typically involve an…
We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all…
Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive…
Unigraphs are graphs identifiable up to isomorphism from their degree sequences. Given a class $\mathcal{A}$ of graphs, we define the class of $\mathcal{A}$-unigraphs to be graphs identifiable from degree sequence and membership in…
We consider the graph whose vertex set is a conjugacy class ${\mathcal C}$ consisting of finite-rank self-adjoint operators on a complex Hilbert space $H$. The dimension of $H$ is assumed to be not less than $3$. In the case when operators…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
The inducibility of a graph $H$ measures the maximum number of induced copies of $H$ a large graph $G$ can have. Generalizing this notion, we study how many induced subgraphs of fixed order $k$ and size $\ell$ a large graph $G$ on $n$…
We compare three transitivity properties of finite graphs, namely, for a positive integer $s$, $s$-distance transitivity, $s$-geodesic transitivity and $s$-arc transitivity. It is known that if a finite graph is $s$-arc transitive but not…
We study online classification under smoothed adversaries. In this setting, at each time point, the adversary draws an example from a distribution that has a bounded density with respect to a fixed base measure, which is known apriori to…
For graph classes $P_1,...,P_k$, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph $G$ can be partitioned into subsets $V_1,...,V_k$ so that $V_j$ induces a graph in the class $P_j$…
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…