Learning Summary Statistics for Bayesian Inference with Autoencoders
This work addresses a bottleneck in Bayesian inference for scientific applications where traditional summary statistics are insufficient, offering a method to enhance computational efficiency and accuracy.
The paper tackles the challenge of selecting informative summary statistics for approximate Bayesian computation in models with intractable likelihoods by proposing autoencoders with noise-aware decoders to encode parameter-related information while filtering out noise, achieving improved posterior approximations as validated on two stochastic models.
For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.