On Dynamical Probabilities, or: How to Learn to Shoot Straight

Wiklicky, Herbert

doi:10.1007/978-3-319-39519-7_16

Cited by 2 publications

(1 citation statement)

References 17 publications

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“…In the probabilistic choices, instead of parameters p ∈ [0, 1] we could have used arbitrary functions p : S → [0, 1] mapping the current program state to a probability as discussed e.g. in [54]. This would not change our semantics fundamentally.…”

Section: The Programming Languagementioning

confidence: 99%

Conditioning in Probabilistic Programming

Olmedo

Gretz

Jansen

et al. 2018

ACM Trans. Program. Lang. Syst.

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This paper investigates the semantic intricacies of conditioning, a main feature in probabilistic programming. Our study is based on an extension of the imperative probabilistic guarded command language pGCL with conditioning. We provide a weakest precondition (wp) semantics and an operational semantics. To deal with possibly diverging program behaviour we consider liberal preconditions. We show that diverging program behaviour plays a key role when defining conditioning. We establish that weakest preconditions coincide with conditional expected rewards in Markov chains-the operational semantics-and that the wp-semantics conservatively extends the existing semantics of pGCL (without conditioning). An extension of these results with non-determinism turns out to be problematic: although an operational semantics using Markov decision processes is rather straightforward, we show that providing an inductive wp-semantics in this setting is impossible. Finally, we present two program transformations which eliminate conditioning from any program. The first transformation hoists conditioning while updating the probabilistic choices in the program, while the second transformation replaces conditioning-in the same vein as rejection sampling-by a program with loops. In addition, we present a last program transformation that replaces an independent identically distributed loop with conditioning.

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Section: The Programming Languagementioning

confidence: 99%