Optimal Design Emulators: A Point Process Approach

Abstract

Design of experiments is a fundamental topic in applied statistics with a long history. Yet its application is often limited by the complexity and costliness of constructing experimental designs, which involve searching a high-dimensional input space and evaluating computationally expensive criterion functions. In this work, we introduce a novel approach to the challenging design problem. We will take a probabilistic view of the problem by representing the optimal design as being one element (or a subset of elements) of a probability space. Given a suitable distribution on this space, a generative point process can be specified from which stochastic design realizations can be drawn. In particular, we describe a scenario where the classical entropy-optimal design for Gaussian Process regression coincides with the mode of a particular point process. We conclude with outlining an algorithm for drawing such design realizations, its extension to sequential designs, and applying the techniques developed to constructing designs for Stochastic Gradient Descent and Gaussian process regression.