5 research outputs found
On the geometry of Stein variational gradient descent
Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely on iterated steepest descent steps with respect to a reproducing kernel Hilbert space norm. This construction leads to interacting particle systems, the mean-field limit of which is a gradient flow on the space of probability distributions equipped with a certain geometrical structure. We leverage this viewpoint to shed some light on the convergence properties of the algorithm, in particular addressing the problem of choosing a suitable positive definite kernel function. Our analysis leads us to considering certain nondifferentiable kernels with adjusted tails. We demonstrate significant performs gains of these in various numerical experiments
On the geometry of Stein variational gradient descent
Bayesian inference problems require sampling or approximating
high-dimensional probability distributions. The focus of this paper is on the
recently introduced Stein variational gradient descent methodology, a class of
algorithms that rely on iterated steepest descent steps with respect to a
reproducing kernel Hilbert space norm. This construction leads to interacting
particle systems, the mean-field limit of which is a gradient flow on the space
of probability distributions equipped with a certain geometrical structure. We
leverage this viewpoint to shed some light on the convergence properties of the
algorithm, in particular addressing the problem of choosing a suitable positive
definite kernel function. Our analysis leads us to considering certain
nondifferentiable kernels with adjusted tails. We demonstrate significant
performs gains of these in various numerical experiments.Comment: 39 pages, 4 figure