21,513 research outputs found
Beyond the grounding bottleneck: Datalog techniques for inference in probabilistic logic programs
State-of-the-art inference approaches in probabilistic logic programming
typically start by computing the relevant ground program with respect to the
queries of interest, and then use this program for probabilistic inference
using knowledge compilation and weighted model counting. We propose an
alternative approach that uses efficient Datalog techniques to integrate
knowledge compilation with forward reasoning with a non-ground program. This
effectively eliminates the grounding bottleneck that so far has prohibited the
application of probabilistic logic programming in query answering scenarios
over knowledge graphs, while also providing fast approximations on classical
benchmarks in the field
Probabilistic Inference Using Partitioned Bayesian Networks:Introducing a Compositional Framework
Probability theory offers an intuitive and formally sound way to reason in situations that involve uncertainty. The automation of probabilistic reasoning has many applications such as predicting future events or prognostics, providing decision support, action planning under uncertainty, dealing with multiple uncertain measurements, making a diagnosis, and so forth. Bayesian networks in particular have been used to represent probability distributions that model the various applications of uncertainty reasoning. However, present-day automated reasoning approaches involving uncertainty struggle when models increase in size and complexity to fit real-world applications.In this thesis, we explore and extend a state-of-the-art automated reasoning method, called inference by Weighted Model Counting (WMC), when applied to increasingly complex Bayesian network models. WMC is comprised of two distinct phases: compilation and inference. The computational cost of compilation has limited the applicability of WMC. To overcome this limitation we have proposed theoretical and practical solutions that have been tested extensively in empirical studies using real-world Bayesian network models.We have proposed a weighted variant of OBDDs, called Weighted Positive Binary Decision Diagrams (WPBDD), which in turn is based on the new notion of positive Shannon decomposition. WPBDDs are particularly well suited to represent discrete probabilistic models. The conciseness of WPBDDs leads to a reduction in the cost of probabilistic inference.We have introduced Compositional Weighted Model Counting (CWMC), a language-agnostic framework for probabilistic inference that partitions a Bayesian network into subproblems. These subproblems are then compiled and subsequently composed in order to perform inference. This approach significantly reduces the cost of compilation, yet increases the cost of inference. The best results are obtained by seeking a partitioning that allows compilation to (barely) become feasible, but no more, as compilation cost can be amortized over multiple inference queries.Theoretical concepts have been implemented in a readily available open-source tool called ParaGnosis. Further implementational improvements have been found through parallelism, by exploiting independencies that are introduced by CWMC. The proposed methods combined push the boundaries of WMC, allowing this state-of-the-art method to be used on much larger models than before
Component Caching in Hybrid Domains with Piecewise Polynomial Densities
Counting the models of a propositional formula is an important problem: for example, it serves as the backbone of probabilistic inference by weighted model counting. A key algorithmic insight is component caching (CC), in which disjoint components of a formula, generated dynamically during a DPLL search, are cached so that they only have to be solved once. In the recent years, driven by SMT technology and probabilistic inference in hybrid domains, there is an increasing interest in counting the models of linear arithmetic sentences. To date, however, solvers for these are block-clause implementations, which are nonviable on large problem instances. In this paper, as a first step in extending CC to hybrid domains, we show how propositional CC systems can be leveraged when limited to piecewise polynomial densities. Our experiments demonstrate a large gap in performance when compared to existing approaches based on a variety of block-clause strategies
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
Probabilistic Program Abstractions
Abstraction is a fundamental tool for reasoning about complex systems.
Program abstraction has been utilized to great effect for analyzing
deterministic programs. At the heart of program abstraction is the relationship
between a concrete program, which is difficult to analyze, and an abstract
program, which is more tractable. Program abstractions, however, are typically
not probabilistic. We generalize non-deterministic program abstractions to
probabilistic program abstractions by explicitly quantifying the
non-deterministic choices. Our framework upgrades key definitions and
properties of abstractions to the probabilistic context. We also discuss
preliminary ideas for performing inference on probabilistic abstractions and
general probabilistic programs
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
Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting
Weighted model counting (WMC) has emerged as a prevalent approach for
probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF
counting (weighted #DNF) is a special case, where approximations with
probabilistic guarantees are obtained in O(nm), where n denotes the number of
variables, and m the number of clauses of the input DNF, but this is not
scalable in practice. In this paper, we propose a neural model counting
approach for weighted #DNF that combines approximate model counting with deep
learning, and accurately approximates model counts in linear time when width is
bounded. We conduct experiments to validate our method, and show that our model
learns and generalizes very well to large-scale #DNF instances.Comment: To appear in Proceedings of the Thirty-Fourth AAAI Conference on
Artificial Intelligence (AAAI-20). Code and data available at:
https://github.com/ralphabb/NeuralDNF
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