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Register a new userA Jump Stochastic Differential Equation Approach for Influence Prediction on Information Propagation Networks
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We propose a novel problem formulation of continuous-time information propagation on heterogenous networks based on jump stochastic differential equations (SDE). The structure of the network and activation rates between nodes are naturally taken into account in the SDE system. This new formulation allows for efficient and stable algorithm for many challenging information propagation problems, including estimations of individual activation probability and influence level, by solving the SDE numerically. To this end, we develop an efficient numerical algorithm incorporating variance reduction; furthermore, we provide theoretical bounds for its sample complexity. Moreover, we show that the proposed jump SDE approach can be applied to a much larger class of critical information propagation problems with more complicated settings. Numerical experiments on a variety of synthetic and real-world propagation networks show that the proposed method is more accurate and efficient compared with the state-of-the-art methods.
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We consider the problem of predicting the time evolution of influence, the expected number of activated nodes, given a set of initially active nodes on a propagation network. To address the significant computational challenges of this problem on large-scale heterogeneous networks, we establish a system of differential equations governing the dynamics of probability mass functions on the state graph where the nodes each lumps a number of activation states of the network, which can be considered as an analogue to the Fokker-Planck equation in continuous space. We provides several methods to estimate the system parameters which depend on the identities of the initially active nodes, network topology, and activation rates etc. The influence is then estimated by the solution of such a system of differential equations. This approach gives rise to a class of novel and scalable algorithms that work effectively for large-scale and dense networks. Numerical results are provided to show the very promising performance in terms of prediction accuracy and computational efficiency of this approach.
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