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For stochastic models with intractable likelihood functions, approximateBayesian computation offers a way of approximating the true posterior throughrepeated comparisons of observations with simulated model outputs in terms of asmall set of summary statistics. These statistics need to retain theinformation that is relevant for constraining the parameters but cancel out thenoise. They can thus be seen as thermodynamic state variables, for generalstochastic models. For many scientific applications, we need strictly moresummary statistics than model parameters to reach a satisfactory approximationof the posterior. Therefore, we propose to use the inner dimension of deepneural network based Autoencoders as summary statistics. To create an incentivefor the encoder to encode all the parameter-related information but not thenoise, we give the decoder access to explicit or implicit information on thenoise that has been used to generate the training data. We validate theapproach empirically on two types of stochastic models.

Learning Summary Statistics for Bayesian Inference with Autoencoders