LFCS seminar: Ohad Kammar: A domain theory for statistical probabilistic programming.
What 


When 
Mar 12, 2019 from 04:00 PM to 05:00 PM 
Where  IF 4.31/4.33 
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I will describe our recent work on statistical probabilistic
programming languages. These are expressive languages for describing
generative Bayesian models of the kinds used in computational
statistics and machine learning. We give an adequate denotational
semantics for a calculus with recursive higherorder types, continuous
probability distributions, and soft constraints. Among them are
untyped languages, similar to Church and WebPPL, because our semantics
allows recursive mixedvariance datatypes. Our semantics justifies
important program equivalences including commutativity.
Our new semantic model is based on `quasiBorel predomains'. These are
a mixture of chaincomplete partial orders (cpos) and quasiBorel
spaces. QuasiBorel spaces are a recent model of probability theory
that focuses on sets of admissible random elements. I will give a
brief introduction to quasiBorel spaces and predomains, and their
properties.
Probability is traditionally treated in cpo models using probabilistic
powerdomains, but these are not known to be commutative on any class
of cpos with higherorder functions. By contrast, quasiBorel
predomains do support both a commutative probabilistic powerdomain and
higherorder functions, which I will describe.
For more details on this joint work with Matthijs Vákár and Sam
Staton, see:
Matthijs Vákár, Ohad Kammar, and Sam Staton. 2019. A Domain Theory for
Statistical Probabilistic Programming. Proc. ACM Program. Lang. 3,
POPL, Article 36 (January 2019), 35 pages., DOI: 10.1145/3290349.