Active Area Search via Bayesian Quadrature

Abstract

The selection of data collection locations is a problem that has received significant research attention from classical design of experiments to various recent active learning algorithms. Typical objectives are to map an unknown function, optimize it, or find level sets in it. Each of these objectives focuses on an assess- ment of individual points. The introduction of set kernels has led to algorithms that in- stead consider labels assigned to sets of data points. In this paper we combine these two concepts and consider the problem of choos- ing data collection locations when the goal is to identify regions whose set of collected data would be labeled positively by a set clas- sifier. We present an algorithm for the case where the positive class is defined in terms of a region’s average function value being above some threshold with high probability, a prob- lem we call active area search. To this end, we model the latent function using a Gaussian process and use Bayesian quadrature to esti- mate its integral on predefined regions. Our method is the first which directly solves the active area search problem. In experiments it outperforms previous algorithms that were developed for other active search goals.