Extending Stan for Deep Probabilistic Programming

Stan is a popular declarative probabilistic programming language with a high-level syntax for expressing graphical models and beyond. Stan differs by nature from generative probabilistic programming languages like Church, Anglican, or Pyro. This paper presents a comprehensive compilation scheme to compile any Stan model to a generative language and proves its correctness. This sheds a clearer light on the relative expressiveness of different kinds of probabilistic languages and opens the door to combining their mutual strengths. Specifically, we use our compilation scheme to build a compiler from Stan to Pyro and extend Stan with support for explicit variational inference guides and deep probabilistic models. That way, users familiar with Stan get access to new features without having to learn a fundamentally new language. Overall, our paper clarifies the relationship between declarative and generative probabilistic programming languages and is a step towards making deep probabilistic programming easier

On the Complexity and Approximation of Binary Evidence in Lifted Inference

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities. The reason is that conditioning on evidence breaks many of the model's symmetries, which can preempt standard lifting techniques. Recent theoretical results show, for example, that conditioning on evidence which corresponds to binary relations is #P-hard, suggesting that no lifting is to be expected in the worst case. In this paper, we balance this negative result by identifying the Boolean rank of the evidence as a key parameter for characterizing the complexity of conditioning in lifted inference. In particular, we show that conditioning on binary evidence with bounded Boolean rank is efficient. This opens up the possibility of approximating evidence by a low-rank Boolean matrix factorization, which we investigate both theoretically and empirically.Comment: To appear in Advances in Neural Information Processing Systems 26 (NIPS), Lake Tahoe, USA, December 201