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 parameterized models and locate plausible regions for the model parameters. By examining multiple data sets, scientists can obtain inferences which typically are much more informative than the deductions derived from each of the data sources independently. Several standard data combination techniques result in target functions which are a weighted sum of the observed data sources. Thus, computing constraints on the plausible regions of the model parameter space can be formulated as finding a level set of a target function which is the sum of observable functions. We propose an active learning algorithm for this problem which selects both a a sample (from the parameter space) and an observable function upon which to compute the next sample. Empirical tests on synthetic functions and on real data for an eight parameter cosmological model show that our algorithm significantly reduces the number of samples required to identify the desired level-set.