8 research outputs found
Compositional Semantics for Probabilistic Programs with Exact Conditioning
We define a probabilistic programming language for Gaussian random variables
with a first-class exact conditioning construct. We give operational,
denotational and equational semantics for this language, establishing
convenient properties like exchangeability of conditions. Conditioning on
equality of continuous random variables is nontrivial, as the exact observation
may have probability zero; this is Borel's paradox. Using categorical
formulations of conditional probability, we show that the good properties of
our language are not particular to Gaussians, but can be derived from universal
properties, thus generalizing to wider settings. We define the Cond
construction, which internalizes conditioning as a morphism, providing general
compositional semantics for probabilistic programming with exact conditioning.Comment: 16 pages, 5 figure
Computable Measure Theory and Algorithmic Randomness
International audienceWe provide a survey of recent results in computable measure and probability theory, from both the perspectives of computable analysis and algorithmic randomness, and discuss the relations between them
Blang: Bayesian declarative modelling of general data structures and inference via algorithms based on distribution continua
Consider a Bayesian inference problem where a variable of interest does not
take values in a Euclidean space. These "non-standard" data structures are in
reality fairly common. They are frequently used in problems involving latent
discrete factor models, networks, and domain specific problems such as sequence
alignments and reconstructions, pedigrees, and phylogenies. In principle,
Bayesian inference should be particularly well-suited in such scenarios, as the
Bayesian paradigm provides a principled way to obtain confidence assessment for
random variables of any type. However, much of the recent work on making
Bayesian analysis more accessible and computationally efficient has focused on
inference in Euclidean spaces.
In this paper, we introduce Blang, a domain specific language and library
aimed at bridging this gap. Blang allows users to perform Bayesian analysis on
arbitrary data types while using a declarative syntax similar to BUGS. Blang is
augmented with intuitive language additions to create data types of the user's
choosing. To perform inference at scale on such arbitrary state spaces, Blang
leverages recent advances in sequential Monte Carlo and non-reversible Markov
chain Monte Carlo methods