Foundation Posteriors for Approximate Probabilistic Inference
This addresses the challenge of efficient and flexible inference for users of probabilistic programming, though it is incremental as it builds on existing neural and variational methods.
The paper tackles the problem of posterior inference in probabilistic programs, which is often computationally expensive and requires many hyper-parameters, by formulating it as masked language modeling and training a neural network to amortize costs, achieving zero-shot and fine-tuned inference on STAN programs with competitive performance.
Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables. Existing techniques for inference in probabilistic programs often require choosing many hyper-parameters, are computationally expensive, and/or only work for restricted classes of programs. Here we formulate inference as masked language modeling: given a program, we generate a supervised dataset of variables and assignments, and randomly mask a subset of the assignments. We then train a neural network to unmask the random values, defining an approximate posterior distribution. By optimizing a single neural network across a range of programs we amortize the cost of training, yielding a "foundation" posterior able to do zero-shot inference for new programs. The foundation posterior can also be fine-tuned for a particular program and dataset by optimizing a variational inference objective. We show the efficacy of the approach, zero-shot and fine-tuned, on a benchmark of STAN programs.