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SUMMARY:A domain theory for statistical probabilistic programming - Ohad K
 ammar\, Edinburgh
DTSTART:20190222T150000Z
DTEND:20190222T160000Z
UID:TALK118606@talks.cam.ac.uk
CONTACT:Victor Gomes
DESCRIPTION:I will describe our recent work on statistical probabilistic\n
 programming languages. These are expressive languages for describing\ngene
 rative Bayesian models of the kinds used in computational\nstatistics and 
 machine learning. We give an adequate denotational\nsemantics for a calcul
 us with recursive higher-order types\, continuous\nprobability distributio
 ns\, and soft constraints.  Among them are\nuntyped languages\, similar to
  Church and WebPPL\, because our semantics\nallows recursive mixed-varianc
 e datatypes.  Our semantics justifies\nimportant program equivalences incl
 uding commutativity.\n\nOur new semantic model is based on `quasi-Borel pr
 edomains'. These are\na mixture of chain-complete partial orders (cpos) an
 d quasi-Borel\nspaces. Quasi-Borel spaces are a recent model of probabilit
 y theory\nthat focuses on sets of admissible random elements. I will give 
 a\nbrief introduction to quasi-Borel spaces and predomains\, and their\npr
 operties.\n\nProbability is traditionally treated in cpo models using prob
 abilistic\npowerdomains\, but these are not known to be commutative on any
  class\nof cpos with higher-order functions. By contrast\, quasi-Borel\npr
 edomains do support both a commutative probabilistic powerdomain and\nhigh
 er-order functions\, which I will describe.\n\nFor more details on this jo
 int work with Matthijs Vákár and Sam\nStaton\, see:\n\nMatthijs Vákár\
 , Ohad Kammar\, and Sam Staton. 2019. A Domain Theory for\nStatistical Pro
 babilistic Programming. Proc. ACM Program. Lang. 3\,\nPOPL\, Article 36 (J
 anuary 2019)\, 35 pages.\, DOI: 10.1145/3290349.
LOCATION:FW26
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