Riemannian Stein Variational Gradient Descent for Bayesian Inference

Abstract

We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean spaces, RSVGD has the advantage over SVGD of utilizing information geometry, and (ii) for inference tasks on Riemann manifolds, RSVGD brings the unique advantages of SVGD to the Riemannian world. To appropriately transfer to Riemann manifolds, we conceive novel and non-trivial techniques for RSVGD, which are required by the intrinsically different characteristics of general Riemann manifolds from Euclidean spaces. We also discover Riemannian Stein's Identity and Riemannian Kernelized Stein Discrepancy. Experimental results show the advantages over SVGD of exploring distribution geometry and the advantages of particle-efficiency, iteration-effectiveness and approximation flexibility over other inference methods on Riemann manifolds.

12 pages, 2 figures, AAAI-18

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Cited by in corpus (10)

• Riemannian Adaptive Optimization Methods
• Hyperspherical Variational Auto-Encoders
• Stein Variational Gradient Descent With Matrix-Valued Kernels
• A Stein variational Newton method
• Diffusion Variational Autoencoders
• Projected Stein Variational Gradient Descent
• Stein variational gradient descent with local approximations
• Minimum Stein Discrepancy Estimators
• Stochastic Particle-Optimization Sampling and the Non-Asymptotic Convergence Theory
• Posterior Integration on a Riemannian Manifold