A Stein variational Newton method
This work addresses the computational efficiency of variational inference methods for machine learning practitioners, representing an incremental improvement over existing SVGD.
The paper tackles the problem of accelerating Stein variational gradient descent (SVGD) for nonparametric variational inference by incorporating second-order information to approximate a Newton-like iteration in function space, resulting in significant computational gains across multiple test cases.
Stein variational gradient descent (SVGD) was recently proposed as a general purpose nonparametric variational inference algorithm [Liu & Wang, NIPS 2016]: it minimizes the Kullback-Leibler divergence between the target distribution and its approximation by implementing a form of functional gradient descent on a reproducing kernel Hilbert space. 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.