A Stein variational Newton method

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Gianluca Detommaso, Tiangang Cui, Youssef Marzouk, Alessio Spantini, Robert Scheichl


Stein variational gradient descent (SVGD) was recently proposed as a general purpose nonparametric variational inference algorithm: it minimizes the KullbackÔÇôLeibler divergence between the target distribution and its approximation by implementing a form of functional gradient descent on a reproducing kernel Hilbert space [Liu & Wang, NIPS 2016]. In this paper, we accelerate and generalize the SVGD algorithm by including second-order information, thereby approximating a Newton-like iteration in function space. We also show how second-order information can lead to more effective choices of kernel. We observe significant computational gains over the original SVGD algorithm in multiple test cases.