603 research outputs found
Symbolic Exact Inference for Discrete Probabilistic Programs
The computational burden of probabilistic inference remains a hurdle for
applying probabilistic programming languages to practical problems of interest.
In this work, we provide a semantic and algorithmic foundation for efficient
exact inference on discrete-valued finite-domain imperative probabilistic
programs. We leverage and generalize efficient inference procedures for
Bayesian networks, which exploit the structure of the network to decompose the
inference task, thereby avoiding full path enumeration. To do this, we first
compile probabilistic programs to a symbolic representation. Then we adapt
techniques from the probabilistic logic programming and artificial intelligence
communities in order to perform inference on the symbolic representation. We
formalize our approach, prove it sound, and experimentally validate it against
existing exact and approximate inference techniques. We show that our inference
approach is competitive with inference procedures specialized for Bayesian
networks, thereby expanding the class of probabilistic programs that can be
practically analyzed
Algebraic model counting
Weighted model counting (WMC) is a well-known inference task on knowledge bases, and the basis for some of the most efficient techniques for probabilistic inference in graphical models. We introduce algebraic model counting (AMC), a generalization of WMC to a semiring structure that provides a unified view on a range of tasks and existing results. We show that AMC generalizes many well-known tasks in a variety of domains such as probabilistic inference, soft constraints and network and database analysis. Furthermore, we investigate AMC from a knowledge compilation perspective and show that all AMC tasks can be evaluated using sd-DNNF circuits, which are strictly more succinct, and thus more efficient to evaluate, than direct representations of sets of models. We identify further characteristics of AMC instances that allow for evaluation on even more succinct circuits
Bayesian network learning with cutting planes
The problem of learning the structure of Bayesian networks from complete
discrete data with a limit on parent set size is considered. Learning is cast
explicitly as an optimisation problem where the goal is to find a BN structure
which maximises log marginal likelihood (BDe score). Integer programming,
specifically the SCIP framework, is used to solve this optimisation problem.
Acyclicity constraints are added to the integer program (IP) during solving in
the form of cutting planes. Finding good cutting planes is the key to the
success of the approach -the search for such cutting planes is effected using a
sub-IP. Results show that this is a particularly fast method for exact BN
learning
- …