Reactive probabilistic programming

International audienceSynchronous modeling is at the heart of programming languages like Lustre, Esterel, or SCADE used routinely for implementing safety critical control software, e.g., fly-bywire and engine control in planes. However, to date these languages have had limited modern support for modeling uncertainty-probabilistic aspects of the software's environment or behavior-even though modeling uncertainty is a primary activity when designing a control system. In this paper we present ProbZelus the first synchronous probabilistic programming language. ProbZelus conservatively provides the facilities of a synchronous language to write control software, with probabilistic constructs to model uncertainties and perform inference-in-the-loop. We present the design and implementation of the language. We propose a measure-theoretic semantics of probabilistic stream functions and a simple type discipline to separate deterministic and probabilistic expressions. We demonstrate a semantics-preserving compilation into a first-order functional language that lends itself to a simple presentation of inference algorithms for streaming models. We also redesign the delayed sampling inference algorithm to provide efficient streaming inference. Together with an evaluation on several reactive applications, our results demonstrate that ProbZelus enables the design of reactive probabilistic applications and efficient, bounded memory inference

Reactive Probabilistic Programming

Synchronous reactive languages were introduced for designing and implementing real-time control software. These domain-specific languages allow for writing a modular and mathematically precise specification of the system, enabling a user to simulate, test, verify, and, finally, compile the system into executable code. However, to date these languages have had limited modern support for modeling uncertainty -- probabilistic aspects of the software's environment or behavior -- even though modeling uncertainty is a primary activity when designing a control system.In this paper we extend Zélus, a synchronous programming language, to deliver ProbZélus, the first synchronous probabilistic programming language. ProbZélus is a probabilistic programming language in that it provides facilities for probabilistic models and inference: inferring latent model parameters from data.We present ProbZélus's measure-theoretic semantics in the setting of probabilistic, stateful stream functions. We then demonstrate a semantics-preserving compilation strategy to a first-order functional core calculus that lends itself to a simple semantic presentation of ProbZélus's inference algorithms. We also redesign the delayed sampling inference algorithm to provide bounded and streaming delayed sampling inference for ProbZélus models. Together with our evaluation on several reactive programs, our results demonstrate that ProbZélus provides efficient, bounded memory probabilistic inference