  Parameter estimation with non-Gaussian stochastic fields is a common
challenge in astrophysics and cosmology. In this paper, we advocate performing
this task using the scattering transform, a statistical tool sharing ideas with
convolutional neural networks (CNNs) but requiring no training nor tuning. It
generates a compact set of coefficients, which can be used as robust summary
statistics for non-Gaussian information. It is especially suited for fields
presenting localized structures and hierarchical clustering, such as the
cosmological density field.
  To demonstrate its power, we apply this estimator to a cosmological parameter
inference problem in the context of weak lensing. On simulated convergence maps
with realistic noise, the scattering transform outperforms classic estimators
and is on a par with state-of-the-art CNN. It retains the advantages of
traditional statistical descriptors, has provable stability properties, allows
to check for systematics, and importantly, the scattering coefficients are
interpretable. It is a powerful and attractive estimator for observational
cosmology and the study of physical fields in general.

Cosmology and Nongalactic Astrophysics;Instrumentation and Methods for Astrophysics