This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with Stein reproducing kernel. Finite-sample-size bounds the error are established distributions supported compact Riemannian manifold, we relate these to kernel discrepancy (KSD). Moreover, prove in our setting that KSD is equivalent Sobolev and, doing so, completely characteri...

We propose a novel adaptive importance sampling algorithm which incorporates Stein variational gradient decent algorithm (SVGD) with importance sampling (IS). Our algorithm leverages the nonparametric transforms in SVGD to iteratively decrease the KL divergence between importance proposals and target distributions. The advantages of our algorithm are twofold: 1) it turns SVGD into a standard IS...

When deriving the estimates on integral operators one often uses the Almost Orthogonality principle of M. Cotlar and E.M. Stein, first proved by M. Cotlar in [Cot55]. This result is classical; our excuse for formulating it once again is a need to have its weighted form which sometimes allows to reduce the number of integrations by parts in half (hereby weakening smoothness requirements), and al...

Donald G. Stein is the Asa G. Candler Professor of Emergency Medicine at the Emory University School of Medicine. He received his BS and MA degrees at Michigan State University and his PhD degree at the University of Oregon. He did his postdoctoral training at Massachusetts Institute of Technology and started his teaching career at Clark University, where began his work in the area of recovery ...