Reactive Probabilistic Programming
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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.
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