The omnipresence of cascading process in complex phenomena makes the identification of a small set of influential units, which is widely believed to trigger the outbreak, always an crucial issue in network science. Formulated as Influence maximization (IM) in 2003, this NP-hard problem has received a multitude of heuristic solutions with diverse angles. However, these methods are often unable to provide reliable solutions, due to the lack of an exact metric for evaluating units' contributions on cascading.

We propose a projected Stein variational Newton (pSVN) method for high-dimensional Bayesian inference. To address the curse of dimensionality, we exploit the intrinsic low-dimensional geometric structure of the posterior distribution in the high-dimensional parameter space via its Hessian (of the log posterior) operator and perform a parallel update of the parameter samples projected into a low-dimensional subspace by an SVN method. The subspace is adaptively constructed using the eigenvectors of the averaged Hessian at the current samples. We demonstrate fast convergence of the proposed method, complexity independent of the parameter and sample dimensions, and parallel scalability.