  We present a probabilistic modeling framework and adaptive sampling algorithm
wherein unsupervised generative models are combined with black box predictive
models to tackle the problem of input design. In input design, one is given one
or more stochastic "oracle" predictive functions, each of which maps from the
input design space (e.g. DNA sequences or images) to a distribution over a
property of interest (e.g. protein fluorescence or image content). Given such
stochastic oracles, the problem is to find an input that is expected to
maximize one or more properties, or to achieve a specified value of one or more
properties, or any combination thereof. We demonstrate experimentally that our
approach substantially outperforms other recently presented methods for
tackling a specific version of this problem, namely, maximization when the
oracle is assumed to be deterministic and unbiased. We also demonstrate that
our method can tackle more general versions of the problem.
