On the Convexity of Latent Social Network Inference

In many real-world scenarios, it is nearly impossible to collect explicit social network data. In such cases, whole networks must be inferred from underlying observations. Here, we formulate the problem of inferring latent social networks based on network diffusion or disease propagation data. We consider contagions propagating over the edges of an unobserved social network, where we only observe the times when nodes became infected, but not who infected them. Given such node infection times, we then identify the optimal network that best explains the observed data. We present a maximum likelihood approach based on convex programming with a l1-like penalty term that encourages sparsity. Experiments on real and synthetic data reveal that our method near-perfectly recovers the underlying network structure as well as the parameters of the contagion propagation model. Moreover, our approach scales well as it can infer optimal networks of thousands of nodes in a matter of minutes.Comment: NIPS, 201

Uncovering the Temporal Dynamics of Diffusion Networks

Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission rates between nodes and transmission sources are unknown. Inferring the underlying dynamics is of outstanding interest since it enables forecasting, influencing and retarding infections, broadly construed. To this end, we model diffusion processes as discrete networks of continuous temporal processes occurring at different rates. Given cascade data -- observed infection times of nodes -- we infer the edges of the global diffusion network and estimate the transmission rates of each edge that best explain the observed data. The optimization problem is convex. The model naturally (without heuristics) imposes sparse solutions and requires no parameter tuning. The problem decouples into a collection of independent smaller problems, thus scaling easily to networks on the order of hundreds of thousands of nodes. Experiments on real and synthetic data show that our algorithm both recovers the edges of diffusion networks and accurately estimates their transmission rates from cascade data.Comment: To appear in the 28th International Conference on Machine Learning (ICML), 2011. Website: http://www.stanford.edu/~manuelgr/netrate

Learning user-specific latent influence and susceptibility from information cascades

Predicting cascade dynamics has important implications for understanding information propagation and launching viral marketing. Previous works mainly adopt a pair-wise manner, modeling the propagation probability between pairs of users using n^2 independent parameters for n users. Consequently, these models suffer from severe overfitting problem, specially for pairs of users without direct interactions, limiting their prediction accuracy. Here we propose to model the cascade dynamics by learning two low-dimensional user-specific vectors from observed cascades, capturing their influence and susceptibility respectively. This model requires much less parameters and thus could combat overfitting problem. Moreover, this model could naturally model context-dependent factors like cumulative effect in information propagation. Extensive experiments on synthetic dataset and a large-scale microblogging dataset demonstrate that this model outperforms the existing pair-wise models at predicting cascade dynamics, cascade size, and "who will be retweeted".Comment: from The 29th AAAI Conference on Artificial Intelligence (AAAI-2015

Submodular Inference of Diffusion Networks from Multiple Trees

Diffusion and propagation of information, influence and diseases take place over increasingly larger networks. We observe when a node copies information, makes a decision or becomes infected but networks are often hidden or unobserved. Since networks are highly dynamic, changing and growing rapidly, we only observe a relatively small set of cascades before a network changes significantly. Scalable network inference based on a small cascade set is then necessary for understanding the rapidly evolving dynamics that govern diffusion. In this article, we develop a scalable approximation algorithm with provable near-optimal performance based on submodular maximization which achieves a high accuracy in such scenario, solving an open problem first introduced by Gomez-Rodriguez et al (2010). Experiments on synthetic and real diffusion data show that our algorithm in practice achieves an optimal trade-off between accuracy and running time.Comment: To appear in the 29th International Conference on Machine Learning (ICML), 2012. Website: http://www.stanford.edu/~manuelgr/network-inference-multitree

Phantom cascades: The effect of hidden nodes on information diffusion

Research on information diffusion generally assumes complete knowledge of the underlying network. However, in the presence of factors such as increasing privacy awareness, restrictions on application programming interfaces (APIs) and sampling strategies, this assumption rarely holds in the real world which in turn leads to an underestimation of the size of information cascades. In this work we study the effect of hidden network structure on information diffusion processes. We characterise information cascades through activation paths traversing visible and hidden parts of the network. We quantify diffusion estimation error while varying the amount of hidden structure in five empirical and synthetic network datasets and demonstrate the effect of topological properties on this error. Finally, we suggest practical recommendations for practitioners and propose a model to predict the cascade size with minimal information regarding the underlying network.Comment: Preprint submitted to Elsevier Computer Communication

Collaborative Inference of Coexisting Information Diffusions

Recently, \textit{diffusion history inference} has become an emerging research topic due to its great benefits for various applications, whose purpose is to reconstruct the missing histories of information diffusion traces according to incomplete observations. The existing methods, however, often focus only on single information diffusion trace, while in a real-world social network, there often coexist multiple information diffusions over the same network. In this paper, we propose a novel approach called Collaborative Inference Model (CIM) for the problem of the inference of coexisting information diffusions. By exploiting the synergism between the coexisting information diffusions, CIM holistically models multiple information diffusions as a sparse 4th-order tensor called Coexisting Diffusions Tensor (CDT) without any prior assumption of diffusion models, and collaboratively infers the histories of the coexisting information diffusions via a low-rank approximation of CDT with a fusion of heterogeneous constraints generated from additional data sources. To improve the efficiency, we further propose an optimal algorithm called Time Window based Parallel Decomposition Algorithm (TWPDA), which can speed up the inference without compromise on the accuracy by utilizing the temporal locality of information diffusions. The extensive experiments conducted on real world datasets and synthetic datasets verify the effectiveness and efficiency of CIM and TWPDA

Latent Self-Exciting Point Process Model for Spatial-Temporal Networks

We propose a latent self-exciting point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches that assume fully observable interactions, here we consider a scenario where certain interaction events lack information about participants. Instead, this information needs to be inferred from the available observations. We develop an efficient approximate algorithm based on variational expectation-maximization to infer unknown participants in an event given the location and the time of the event. We validate the model on synthetic as well as real-world data, and obtain very promising results on the identity-inference task. We also use our model to predict the timing and participants of future events, and demonstrate that it compares favorably with baseline approaches.Comment: 20 pages, 6 figures (v3); 11 pages, 6 figures (v2); previous version appeared in the 9th Bayesian Modeling Applications Workshop, UAI'1