On proportional volume sampling for experimental design in general spaces

Understand

Optimal design for linear regression is a fundamental task in statistics.

• For finite design spaces, recent progress has shown that random designs drawn using proportional volume sampling (PVS) lead to approximation guarantees for A-optimal design.
• PVS strikes the balance between design nodes that jointly fill the design space, while marginally staying in regions of high mass under the solution of a relaxed convex version of the original problem.
• In this paper, we examine some of the statistical implications of a new variant of PVS for (possibly Bayesian) optimal design.