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arXiv · 1810.04946

A Riemann-Stein Kernel Method

Alessandro Barp·Chris. J. Oates·Emilio Porcu·Mark Girolami
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Abstract

This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation error are established for posterior distributions supported on a compact Riemannian manifold, and we relate these to a kernel Stein discrepancy (KSD). Moreover, we prove in our setting that the KSD is equivalent to Sobolev discrepancy and, in doing so, we completely characterise the convergence-determining properties of KSD. Our contribution is rooted in a novel combination of Stein's method, the theory of reproducing kernels, and existence and regularity results for partial differential equations on a Riemannian manifold.

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Alessandro Barp, Chris. J. Oates, Emilio Porcu, Mark Girolami. 2018-10-11. A Riemann-Stein Kernel Method. https://arxiv.org/abs/1810.04946

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