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

Structure and Dynamics of Information Pathways in Online Media

Diffusion of information, spread of rumors and infectious diseases are all instances of stochastic processes that occur over the edges of an underlying network. Many times networks over which contagions spread are unobserved, and such networks are often dynamic and change over time. In this paper, we investigate the problem of inferring dynamic networks based on information diffusion data. We assume there is an unobserved dynamic network that changes over time, while we observe the results of a dynamic process spreading over the edges of the network. The task then is to infer the edges and the dynamics of the underlying network. We develop an on-line algorithm that relies on stochastic convex optimization to efficiently solve the dynamic network inference problem. We apply our algorithm to information diffusion among 3.3 million mainstream media and blog sites and experiment with more than 179 million different pieces of information spreading over the network in a one year period. We study the evolution of information pathways in the online media space and find interesting insights. Information pathways for general recurrent topics are more stable across time than for on-going news events. Clusters of news media sites and blogs often emerge and vanish in matter of days for on-going news events. Major social movements and events involving civil population, such as the Libyan's civil war or Syria's uprise, lead to an increased amount of information pathways among blogs as well as in the overall increase in the network centrality of blogs and social media sites.Comment: To Appear at the 6th International Conference on Web Search and Data Mining (WSDM '13

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

Modeling Information Propagation with Survival Theory

Networks provide a skeleton for the spread of contagions, like, information, ideas, behaviors and diseases. Many times networks over which contagions diffuse are unobserved and need to be inferred. Here we apply survival theory to develop general additive and multiplicative risk models under which the network inference problems can be solved efficiently by exploiting their convexity. Our additive risk model generalizes several existing network inference models. We show all these models are particular cases of our more general model. Our multiplicative model allows for modeling scenarios in which a node can either increase or decrease the risk of activation of another node, in contrast with previous approaches, which consider only positive risk increments. We evaluate the performance of our network inference algorithms on large synthetic and real cascade datasets, and show that our models are able to predict the length and duration of cascades in real data.Comment: To appear at ICML '1

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