Statistical inference framework for source detection of contagion processes on arbitrary network structures

In this paper we introduce a statistical inference framework for estimating the contagion source from a partially observed contagion spreading process on an arbitrary network structure. The framework is based on a maximum likelihood estimation of a partial epidemic realization and involves large scale simulation of contagion spreading processes from the set of potential source locations. We present a number of different likelihood estimators that are used to determine the conditional probabilities associated to observing partial epidemic realization with particular source location candidates. This statistical inference framework is also applicable for arbitrary compartment contagion spreading processes on networks. We compare estimation accuracy of these approaches in a number of computational experiments performed with the SIR (susceptible-infected-recovered), SI (susceptible-infected) and ISS (ignorant-spreading-stifler) contagion spreading models on synthetic and real-world complex networks

Estimating Infection Sources in Networks Using Partial Timestamps

We study the problem of identifying infection sources in a network based on the network topology, and a subset of infection timestamps. In the case of a single infection source in a tree network, we derive the maximum likelihood estimator of the source and the unknown diffusion parameters. We then introduce a new heuristic involving an optimization over a parametrized family of Gromov matrices to develop a single source estimation algorithm for general graphs. Compared with the breadth-first search tree heuristic commonly adopted in the literature, simulations demonstrate that our approach achieves better estimation accuracy than several other benchmark algorithms, even though these require more information like the diffusion parameters. We next develop a multiple sources estimation algorithm for general graphs, which first partitions the graph into source candidate clusters, and then applies our single source estimation algorithm to each cluster. We show that if the graph is a tree, then each source candidate cluster contains at least one source. Simulations using synthetic and real networks, and experiments using real-world data suggest that our proposed algorithms are able to estimate the true infection source(s) to within a small number of hops with a small portion of the infection timestamps being observed.Comment: 15 pages, 15 figures, accepted by IEEE Transactions on Information Forensics and Securit

Contagion Source Detection in Epidemic and Infodemic Outbreaks: Mathematical Analysis and Network Algorithms

This monograph provides an overview of the mathematical theories and computational algorithm design for contagion source detection in large networks. By leveraging network centrality as a tool for statistical inference, we can accurately identify the source of contagions, trace their spread, and predict future trajectories. This approach provides fundamental insights into surveillance capability and asymptotic behavior of contagion spreading in networks. Mathematical theory and computational algorithms are vital to understanding contagion dynamics, improving surveillance capabilities, and developing effective strategies to prevent the spread of infectious diseases and misinformation.Comment: Suggested Citation: Chee Wei Tan and Pei-Duo Yu (2023), "Contagion Source Detection in Epidemic and Infodemic Outbreaks: Mathematical Analysis and Network Algorithms", Foundations and Trends in Networking: Vol. 13: No. 2-3, pp 107-251. http://dx.doi.org/10.1561/130000006

$1.00 per RT #BostonMarathon #PrayForBoston: analyzing fake content on Twitter

This study found that 29% of the most viral content on Twitter during the Boston bombing crisis were rumors and fake content.AbstractOnline social media has emerged as one of the prominent channels for dissemination of information during real world events. Malicious content is posted online during events, which can result in damage, chaos and monetary losses in the real world. We analyzed one such media i.e. Twitter, for content generated during the event of Boston Marathon Blasts, that occurred on April, 15th, 2013. A lot of fake content and malicious profiles originated on Twitter network during this event. The aim of this work is to perform in-depth characterization of what factors influenced in malicious content and profiles becoming viral. Our results showed that 29% of the most viral content on Twitter, during the Boston crisis were rumors and fake content; while 51% was generic opinions and comments; and rest was true information. We found that large number of users with high social reputation and verified accounts were responsible for spreading the fake content. Next, we used regression prediction model, to verify that, overall impact of all users who propagate the fake content at a given time, can be used to estimate the growth of that content in future. Many malicious accounts were created on Twitter during the Boston event, that were later suspended by Twitter. We identified over six thousand such user profiles, we observed that the creation of such profiles surged considerably right after the blasts occurred. We identified closed community structure and star formation in the interaction network of these suspended profiles amongst themselves

Tree Sampling for Detection of Information Source in Densely Connected Networks

We investigate the problem of source detection in information spreading throughout a densely-connected network. Previous works have been developed mostly for tree networks or applied the tree-network results to non-tree networks assuming that the infection occurs in the breadth first manner. However, these approaches result in low detection performance in densely-connected networks, since there is a substantial number of nodes that are infected through the non-shortest path. In this work, we take a two-step approach to the source detection problem in densely-connected networks. By introducing the concept of detour nodes, we first sample trees that the infection process likely follows and effectively compare the probability of the sampled trees. Our solution has low complexity of O(n2logn, where n denotes the number of infected nodes, and thus can be applied to large-scale networks. Through extensive simulations including practical networks of the Internet autonomous system and power grid, we evaluate our solution in comparison with two well-known previous schemes and show that it achieves the best performance in densely-connected networks

Information extraction with network centralities : finding rumor sources, measuring influence, and learning community structure

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 193-197).Network centrality is a function that takes a network graph as input and assigns a score to each node. In this thesis, we investigate the potential of network centralities for addressing inference questions arising in the context of large-scale networked data. These questions are particularly challenging because they require algorithms which are extremely fast and simple so as to be scalable, while at the same time they must perform well. It is this tension between scalability and performance that this thesis aims to resolve by using appropriate network centralities. Specifically, we solve three important network inference problems using network centrality: finding rumor sources, measuring influence, and learning community structure. We develop a new network centrality called rumor centrality to find rumor sources in networks. We give a linear time algorithm for calculating rumor centrality, demonstrating its practicality for large networks. Rumor centrality is proven to be an exact maximum likelihood rumor source estimator for random regular graphs (under an appropriate probabilistic rumor spreading model). For a wide class of networks and rumor spreading models, we prove that it is an accurate estimator. To establish the universality of rumor centrality as a source estimator, we utilize techniques from the classical theory of generalized Polya's urns and branching processes. Next we use rumor centrality to measure influence in Twitter. We develop an influence score based on rumor centrality which can be calculated in linear time. To justify the use of rumor centrality as the influence score, we use it to develop a new network growth model called topological network growth. We find that this model accurately reproduces two important features observed empirically in Twitter retweet networks: a power-law degree distribution and a superstar node with very high degree. Using these results, we argue that rumor centrality is correctly quantifying the influence of users on Twitter. These scores form the basis of a dynamic influence tracking engine called Trumor which allows one to measure the influence of users in Twitter or more generally in any networked data. Finally we investigate learning the community structure of a network. Using arguments based on social interactions, we determine that the network centrality known as degree centrality can be used to detect communities. We use this to develop the leader-follower algorithm (LFA) which can learn the overlapping community structure in networks. The LFA runtime is linear in the network size. It is also non-parametric, in the sense that it can learn both the number and size of communities naturally from the network structure without requiring any input parameters. We prove that it is very robust and learns accurate community structure for a broad class of networks. We find that the LFA does a better job of learning community structure on real social and biological networks than more common algorithms such as spectral clustering.by Tauhid R. Zaman.Ph.D