Keywords: likelihood-free inference, bayesian inference, mutual information, representation learning, summary statistics
Abstract: We consider the fundamental problem of how to automatically construct summary statistics for implicit generative models where the evaluation of the likelihood function is intractable but sampling data from the model is possible. The idea is to frame the task of constructing sufficient statistics as learning mutual information maximizing representations of the data with the help of deep neural networks. The infomax learning procedure does not need to estimate any density or density ratio. We apply our approach to both traditional approximate Bayesian computation and recent neural likelihood methods, boosting their performance on a range of tasks.
One-sentence Summary: We learn low-dimensional near-sufficient statistics for implicit models by infomax principle without estimating the density or even the density ratio.
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