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.

Convergence of existing Stein variational methods is known to suffer in high dimensions due to the locality of the kernel. The authors address this problem by exploiting the structure of the posterior distribution. Concretely, they propose to perform Stein gradient steps in a low-dimensional projection subspace. The basis of the projection space is derived from the expected Hessian of the log-likelihood, where the expectation is adaptively approximated by an empirical estimate. The introduced projection scheme and the corresponding Stein gradient steps are well motivated and presented. A theoretical analysis is presented to bound the bias introduced by the projection.

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.

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. Papers published at the Neural Information Processing Systems Conference.