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Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…
Processes such as disease propagation and information diffusion often spread over some latent network structure which must be learned from observation. Given a set of unlabeled training examples representing occurrences of an event type of…
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…
Recently, graph anomaly detection on attributed networks has attracted growing attention in data mining and machine learning communities. Apart from attribute anomalies, graph anomaly detection also aims at suspicious topological-abnormal…
In this paper we study the random geometric graph $\mathsf{RGG}(n,\mathbb{T}^d,\mathsf{Unif},\sigma^q_p,p)$ with $L_q$ distance where each vertex is sampled uniformly from the $d$-dimensional torus and where the connection radius is chosen…
We study fundamental graph parameters such as the Diameter and Radius in directed graphs, when distances are measured using a somewhat unorthodox but natural measure: the distance between $u$ and $v$ is the minimum of the shortest path…
For approximate nearest neighbor search, graph-based algorithms have shown to offer the best trade-off between accuracy and search time. We propose the Dynamic Exploration Graph (DEG) which significantly outperforms existing algorithms in…
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…
A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
In this paper, a class of statistics named ART (the alternant recursive topology statistics) is proposed to measure the properties of correlation between two variables. A wide range of bi-variable correlations both linear and nonlinear can…
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
We present a novel method for image anomaly detection, where algorithms that use samples drawn from some distribution of "normal" data, aim to detect out-of-distribution (abnormal) samples. Our approach includes a combination of encoder and…
This paper studies graph-based active learning, where the goal is to reconstruct a binary signal defined on the nodes of a weighted graph, by sampling it on a small subset of the nodes. A new sampling algorithm is proposed, which…
We consider classes of pseudo-random graphs on $n$ vertices for which the degree of every vertex and the co-degree between every pair of vertices are in the intervals $(np - Cn^\delta,np+Cn^\delta)$ and $(np^2- C n^\delta, np^2 +C…
Recently [Bhattacharya et al., STOC 2015] provide the first non-trivial algorithm for the densest subgraph problem in the streaming model with additions and deletions to its edges, i.e., for dynamic graph streams. They present a…
This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on…
Relative efficiency (RE), the Pitman asymptotic relative efficiency (ARE) and efficacy are important relative performance measures of signal detection techniques. These measures allow comparing two detectors in terms of the relative sample…