Meta-Learning an Inference Algorithm for Probabilistic Programs

We present a meta-algorithm for learning a posterior-inference algorithm for restricted probabilistic programs. Our meta-algorithm takes a training set of probabilistic programs that describe models with observations, and attempts to learn an efficient method for inferring the posterior of a similar program. A key feature of our approach is the use of what we call a white-box inference algorithm that extracts information directly from model descriptions themselves, given as programs. Concretely, our white-box inference algorithm is equipped with multiple neural networks, one for each type of atomic command, and computes an approximate posterior of a given probabilistic program by analysing individual atomic commands in the program using these networks. The parameters of these networks are then learnt from a training set by our meta-algorithm. We empirically demonstrate that the learnt inference algorithm generalises well to unseen programs in terms of both interpolation and extrapolation, and report cases where our approach may be preferable to a state-of-the-art inference algorithm such as HMC. The overall results show the promise as well as remaining challenges of our approach.