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

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What
  • LFCS Seminar
  • Upcoming events
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 higher-order types, continuous
probability distributions, and soft constraints.  Among them are
untyped languages, similar to Church and WebPPL, because our semantics
allows recursive mixed-variance datatypes.  Our semantics justifies
important program equivalences including commutativity.

Our new semantic model is based on `quasi-Borel predomains'. These are
a mixture of chain-complete partial orders (cpos) and quasi-Borel
spaces. Quasi-Borel spaces are a recent model of probability theory
that focuses on sets of admissible random elements. I will give a
brief introduction to quasi-Borel 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 higher-order functions. By contrast, quasi-Borel
predomains do support both a commutative probabilistic powerdomain and
higher-order 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.

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