Sampling with Mirrored Stein Operators
This work addresses sampling challenges in constrained domains for applications like post-selection inference, though it appears incremental as it builds on existing Stein variational methods.
The authors tackled the problem of sampling from constrained target distributions and non-Euclidean geometries by introducing new particle evolution samplers, resulting in more rapid convergence than prior methods and accurate approximations for distributions on the simplex.
We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL) divergence to constrained target distributions by evolving particles in a dual space defined by a mirror map. Stein Variational Natural Gradient exploits non-Euclidean geometry to more efficiently minimize the KL divergence to unconstrained targets. We derive these samplers from a new class of mirrored Stein operators and adaptive kernels developed in this work. We demonstrate that these new samplers yield accurate approximations to distributions on the simplex, deliver valid confidence intervals in post-selection inference, and converge more rapidly than prior methods in large-scale unconstrained posterior inference. Finally, we establish the convergence of our new procedures under verifiable conditions on the target distribution.