Abstract
Bayesian networks are graphical first-order probabilistic models that allow for a compact representation of large probability distributions, and for efficient inference, both exact and approximate. We introduce a higher-order programming language, in the idealized form of a lambda-calculus, which we prove sound and complete w.r.t. Bayesian networks: each Bayesian network can be encoded as a term, and conversely each (possibly higher-order and recursive) program of ground type compiles into a Bayesian network. The language allows for the specification of recursive probability models and hierarchical structures. Moreover, we provide a compositional and cost-aware semantics which is based on factors, the standard mathematical tool used in Bayesian inference. Our results rely on advanced techniques rooted into linear logic, intersection types, rewriting theory, and Girard's geometry of interaction, which are here combined in a novel way.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.