  For stochastic models with intractable likelihood functions, approximate
Bayesian computation offers a way of approximating the true posterior through
repeated comparisons of observations with simulated model outputs in terms of a
small set of summary statistics. These statistics need to retain the
information that is relevant for constraining the parameters but cancel out the
noise. They can thus be seen as thermodynamic state variables, for general
stochastic models. For many scientific applications, we need strictly more
summary statistics than model parameters to reach a satisfactory approximation
of the posterior. Therefore, we propose to use the inner dimension of deep
neural network based Autoencoders as summary statistics. To create an incentive
for the encoder to encode all the parameter-related information but not the
noise, we give the decoder access to explicit or implicit information on the
noise that has been used to generate the training data. We validate the
approach empirically on two types of stochastic models.
