  Complex computer simulations are commonly required for accurate data
modelling in many scientific disciplines, making statistical inference
challenging due to the intractability of the likelihood evaluation for the
observed data. Furthermore, sometimes one is interested on inference drawn over
a subset of the generative model parameters while taking into account model
uncertainty or misspecification on the remaining nuisance parameters. In this
work, we show how non-linear summary statistics can be constructed by
minimising inference-motivated losses via stochastic gradient descent such they
provided the smallest uncertainty for the parameters of interest. As a use
case, the problem of confidence interval estimation for the mixture coefficient
in a multi-dimensional two-component mixture model (i.e. signal vs background)
is considered, where the proposed technique clearly outperforms summary
statistics based on probabilistic classification, which are a commonly used
alternative but do not account for the presence of nuisance parameters.
