Neural Approximate Sufficient Statistics for Implicit Models

We consider the fundamental problem of how to automatically construct summary statistics for likelihood-free inference where the evaluation of likelihood function is intractable but sampling / simulating data from the model is possible. The idea is to frame the task of constructing sufficient statistics as learning mutual information maximizing representation of the data. This representation is computed by a deep neural network trained by a joint statistic-posterior learning strategy. We apply our approach to both traditional approximate Bayesian computation and recent neural-likelihood methods, boosting their performance on a wide range of tasks.