Actively Learning Level-Sets of Composite Functions

Abstract

Scientists frequently have multiple types of experiments and data sets on which they can test the validity of their parametrized models and locate plausible regions for the model parameters. By examining multiple data sets, these scientists can obtain inferences for their problems which typically are much more informative than the deductions derived from each of the data sources independently. Several standard data combination techniques result in a target function which is a weighted sum of the observed data sources. Computing constraints on the plausible regions of the model parameter space can be formulated as that of finding a specified level set of the target function. We propose an active learning algorithm for this problem which at each step selects both a parameter setting (from the parameter space) and an experiment type upon which to compute the next sample. Empirical tests on synthetic functions and on real data for a eight parameter cosmological model show that our algorithm significantly reduces the number of samples required to identify desired regions.