On proportional volume sampling for experimental design in general spaces

Optimal design for linear regression is a fundamental task in statistics. For finite spaces, recent progress has shown that random designs drawn using proportional volume sampling (PVS short) lead to polynomial-time algorithms with approximation guarantees outperform i.i.d. sampling. PVS strikes the balance between nodes jointly fill space, while marginally staying regions of high mass under solution relaxed convex version original problem. In this paper, we examine some statistical implications new variant (possibly Bayesian) optimal design. Using point process machinery, treat case generic Polish space. We show not only are known A-optimality preserved, but obtain similar D-optimal tighten results. Moreover, our can be sampled polynomial time. Unfortunately, spite its elegance and tractability, demonstrate on simple example practical general likely limited. second part focus applications investigate use as subroutine stochastic search heuristics. robust addition practitioner’s toolbox, especially when functions nonstandard low-dimensional, complicated shape (e.g., nonlinear boundaries, several connected components).