  Deep learning algorithms have recently shown to be a successful tool in
estimating parameters of statistical models for which simulation is easy, but
likelihood computation is challenging. But the success of these approaches
depends on simulating parameters that sufficiently reproduce the observed data,
and, at present, there is a lack of efficient methods to produce these
simulations. We develop new black-box procedures to estimate parameters of
statistical models based only on weak parameter structure assumptions. For
well-structured likelihoods with frequent occurrences, such as in time series,
this is achieved by pre-training a deep neural network on an extensive
simulated database that covers a wide range of data sizes. For other types of
complex dependencies, an iterative algorithm guides simulations to the correct
parameter region in multiple rounds. These approaches can successfully estimate
and quantify the uncertainty of parameters from non-Gaussian models with
complex spatial and temporal dependencies. The success of our methods is a
first step towards a fully flexible automatic black-box estimation framework.

Machine Learning;Machine Learning