1,569 research outputs found
Computable de Finetti measures
We prove a computable version of de Finetti's theorem on exchangeable
sequences of real random variables. As a consequence, exchangeable stochastic
processes expressed in probabilistic functional programming languages can be
automatically rewritten as procedures that do not modify non-local state. Along
the way, we prove that a distribution on the unit interval is computable if and
only if its moments are uniformly computable.Comment: 32 pages. Final journal version; expanded somewhat, with minor
corrections. To appear in Annals of Pure and Applied Logic. Extended abstract
appeared in Proceedings of CiE '09, LNCS 5635, pp. 218-23
Probabilistic Operational Semantics for the Lambda Calculus
Probabilistic operational semantics for a nondeterministic extension of pure
lambda calculus is studied. In this semantics, a term evaluates to a (finite or
infinite) distribution of values. Small-step and big-step semantics are both
inductively and coinductively defined. Moreover, small-step and big-step
semantics are shown to produce identical outcomes, both in call-by- value and
in call-by-name. Plotkin's CPS translation is extended to accommodate the
choice operator and shown correct with respect to the operational semantics.
Finally, the expressive power of the obtained system is studied: the calculus
is shown to be sound and complete with respect to computable probability
distributions.Comment: 35 page
CHR(PRISM)-based Probabilistic Logic Learning
PRISM is an extension of Prolog with probabilistic predicates and built-in
support for expectation-maximization learning. Constraint Handling Rules (CHR)
is a high-level programming language based on multi-headed multiset rewrite
rules.
In this paper, we introduce a new probabilistic logic formalism, called
CHRiSM, based on a combination of CHR and PRISM. It can be used for high-level
rapid prototyping of complex statistical models by means of "chance rules". The
underlying PRISM system can then be used for several probabilistic inference
tasks, including probability computation and parameter learning. We define the
CHRiSM language in terms of syntax and operational semantics, and illustrate it
with examples. We define the notion of ambiguous programs and define a
distribution semantics for unambiguous programs. Next, we describe an
implementation of CHRiSM, based on CHR(PRISM). We discuss the relation between
CHRiSM and other probabilistic logic programming languages, in particular PCHR.
Finally we identify potential application domains
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