  In many cosmological inference problems, the likelihood (the probability of
the observed data as a function of the unknown parameters) is unknown or
intractable. This necessitates approximations and assumptions, which can lead
to incorrect inference of cosmological parameters, including the nature of dark
matter and dark energy, or create artificial model tensions. Likelihood-free
inference covers a novel family of methods to rigorously estimate posterior
distributions of parameters using forward modelling of mock data. We present
likelihood-free cosmological parameter inference using weak lensing maps from
the Dark Energy Survey (DES) SV data, using neural data compression of weak
lensing map summary statistics. We explore combinations of the power spectra,
peak counts, and neural compressed summaries of the lensing mass map using deep
convolution neural networks. We demonstrate methods to validate the inference
process, for both the data modelling and the probability density estimation
steps. Likelihood-free inference provides a robust and scalable alternative for
rigorous large-scale cosmological inference with galaxy survey data (for DES,
Euclid and LSST). We have made our simulated lensing maps publicly available.
