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Structure discovery in graphical models is the determination of the topology of a graph that encodes conditional independence properties of the joint distribution of all variables in the model. For some class of probability distributions,…
Given independent random points $\mathcal{X}_n=\{X_1,...,X_n\}$ in $\mathbb{R}^2$, drawn according to some probability density function $f$ on $\mathbb{R}^2$, and a cutoff $r_n>0$ we construct a random geometric digraph…
Let $G_n$ be a random geometric graph with vertex set $[n]$ based on $n$ i.i.d.\ random vectors $X_1,\ldots,X_n$ drawn from an unknown density $f$ on $\R^d$. An edge $(i,j)$ is present when $\|X_i -X_j\| \le r_n$, for a given threshold…
We propose a valid and consistent test for the hypothesis that two latent distance random graphs on the same vertex set have the same generating latent positions, up to some unidentifiable similarity transformations. Our test statistic is…
We present a novel hierarchical graph clustering algorithm inspired by modularity-based clustering techniques. The algorithm is agglomerative and based on a simple distance between clusters induced by the probability of sampling node pairs.…
Respondent-Driven Sampling (RDS) employs a variant of a link-tracing network sampling strategy to collect data from hard-to-reach populations. By tracing the links in the underlying social network, the process exploits the social structure…
Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard…
Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" under the framework of the generalized random dot product…
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…
The dominating set problem and its generalization, the distance-$r$ dominating set problem, are among the well-studied problems in the sequential settings. In distributed models of computation, unlike for domination, not much is known about…
We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate…
Ron et al (1998) introduced a rich family of models for discrete longitudinal data, called acyclic probabilistic finite automata. These may be described as context-specific graphical models, since they are represented as directed…
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
Artificial neural networks are prone to being fooled by carefully perturbed inputs which cause an egregious misclassification. These \textit{adversarial} attacks have been the focus of extensive research. Likewise, there has been an…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
The concept of statistical convergence based on asymptotic density is introduced in this article through nets. Some possible extensions of classical results for statistical convergence of sequences are obtained in this article, with…
How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…