Network topology inference using information cascades with limited statistical knowledge

Abstract

We study the problem of inferring network topology from information cascades, in which the amount of time taken for information to diffuse across an edge in the network follows an unknown distribution.Unlike previous studies, which assume knowledge of these distributions, we only require that diffusion along different edges in the network be independent together with limited moment information (e.g., the means). We introduce the concept of a separating vertex set for a graph, which is a set of vertices in which for any two given distinct vertices of the graph, there exists a vertex whose distance to them are different. We show that a necessary condition for reconstructing a tree perfectly using distance information between pairs of vertices is given by the size of an observed separating vertex set. We then propose an algorithm to recover the tree structure using infection times, whose differences have means corresponding to the distance between two vertices. To improve the accuracy of our algorithm, we propose the concept of redundant vertices, which allows us to perform averaging to better estimate the distance between two vertices. Though the theory is developed mainly for tree networks, we demonstrate how the algorithm can be extended heuristically to general graphs. Simulations using synthetic and real networks, and experiments using real-world data suggest that our proposed algorithm performs better than some current state-of-the-art network reconstruction methods.

Joint Inference of Diffusion and Structure in Partially Observed Social Networks Using Coupled Matrix Factorization

“…Structure inference: When the interaction topology of a network is entirely unreachable, an inference approach is put forward using visible independent measurements [14], utilizing the process over the network or with the help of received signals from nodes to infer their connections. Many attempts have been made to solve this problem only based on diffusion knowledge, from static assumption requiring time stamp [15], [16], [17], [18] or without infection time [19] to dynamic inference [20], [21]. As a step further towards using prior knowledge, some works employ in-degree distribution for nodes [22], and measurements such as pathways, network properties, and information about the links or nodes [23].…”

Signal Processing on Simplicial Complexes With Vertex Signals

“…Moreover, in many applications, a graph learning procedure is involved based on information such as geometric distance, vertex feature similarity and graph signals [17]- [21]. Due to the lack of a definite meaning for edge connections, it is arguable whether a graph is the best geometric object for signal processing.…”

Identifying misinformation and their sources in social networks

“…Before presenting our approach, we refer the reader to paper [97] Section III and V for some important concepts and theories. We develop the underlying theory and procedure for the case where only distance information is available.…”

“…We skip such technical results, the interested reader can refer to paper [97] for more details and intuitions. We will also include more intuitions in the following sections so that it does not affect the logic flow.…”

“…We summarise the theoretical discussion in paper [97] Section VI-A and VI-B in the following dichotomy: when the graph is sparse (as measured by the edge to node ratio, for example) or the distributions of the propagation times along each edge have small variance, it is enough to use the mean of the distributions as in the…”