39,884 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
Descriptive Complexity for Counting Complexity Classes
Descriptive Complexity has been very successful in characterizing complexity
classes of decision problems in terms of the properties definable in some
logics. However, descriptive complexity for counting complexity classes, such
as FP and #P, has not been systematically studied, and it is not as developed
as its decision counterpart. In this paper, we propose a framework based on
Weighted Logics to address this issue. Specifically, by focusing on the natural
numbers we obtain a logic called Quantitative Second Order Logics (QSO), and
show how some of its fragments can be used to capture fundamental counting
complexity classes such as FP, #P and FPSPACE, among others. We also use QSO to
define a hierarchy inside #P, identifying counting complexity classes with good
closure and approximation properties, and which admit natural complete
problems. Finally, we add recursion to QSO, and show how this extension
naturally captures lower counting complexity classes such as #L
Inference in Probabilistic Logic Programs using Weighted CNF's
Probabilistic logic programs are logic programs in which some of the facts
are annotated with probabilities. Several classical probabilistic inference
tasks (such as MAP and computing marginals) have not yet received a lot of
attention for this formalism. The contribution of this paper is that we develop
efficient inference algorithms for these tasks. This is based on a conversion
of the probabilistic logic program and the query and evidence to a weighted CNF
formula. This allows us to reduce the inference tasks to well-studied tasks
such as weighted model counting. To solve such tasks, we employ
state-of-the-art methods. We consider multiple methods for the conversion of
the programs as well as for inference on the weighted CNF. The resulting
approach is evaluated experimentally and shown to improve upon the
state-of-the-art in probabilistic logic programming
Lifted Variable Elimination for Probabilistic Logic Programming
Lifted inference has been proposed for various probabilistic logical
frameworks in order to compute the probability of queries in a time that
depends on the size of the domains of the random variables rather than the
number of instances. Even if various authors have underlined its importance for
probabilistic logic programming (PLP), lifted inference has been applied up to
now only to relational languages outside of logic programming. In this paper we
adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the
problem of computing the probability of queries to probabilistic logic programs
under the distribution semantics. In particular, we extend the Prolog Factor
Language (PFL) to include two new types of factors that are needed for
representing ProbLog programs. These factors take into account the existing
causal independence relationships among random variables and are managed by the
extension to variable elimination proposed by Zhang and Poole for dealing with
convergent variables and heterogeneous factors. Two new operators are added to
GC-FOVE for treating heterogeneous factors. The resulting algorithm, called
LP for Lifted Probabilistic Logic Programming, has been implemented by
modifying the PFL implementation of GC-FOVE and tested on three benchmarks for
lifted inference. A comparison with PITA and ProbLog2 shows the potential of
the approach.Comment: To appear in Theory and Practice of Logic Programming (TPLP). arXiv
admin note: text overlap with arXiv:1402.0565 by other author
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