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 gener
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