Manifold Sampling with Automatic Tuning

Many statistical and applied problems involve sampling from distributions constrained to curved lower-dimensional spaces, or manifolds. Standard MCMC methods are inapplicable in these settings because they do not naturally respect the constraint geometry, while existing manifold samplers can be highly sensitive to step-size tuning.

Our main contribution is an automatically tuned manifold sampler with a local step-size selection procedure that adapts to the geometry of the manifold. Under regularity conditions, we show that our method is invariant using the involutive MCMC framework. We further implement a contour-based sampling method with automatic tuning that achieves strong performance in terms of effective sample size per second while maintaining stable acceptance rates on several challenging target distributions. Empirical results show that automatic tuning can make manifold sampling more reliable and less sensitive to step-size choice for constrained and contour-based inference problems.

To join this seminar virtually, please request Zoom connection details from hr.ops@stat.ubc.ca.