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Complexity analysis and variational inference for interpretationbased probabilistic description logics
 IN CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 2009
"... This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies. Inference is shown to be PEXPcomplete, and variational methods ..."
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This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies. Inference is shown to be PEXPcomplete, and variational methods are designed so as to exploit logical inference whenever possible.
Inference in Probabilistic Ontologies with Attributive Concept Descriptions and Nominals
"... Abstract. This paper proposes a probabilistic description logic that combines (i) constructs of the wellknown ALC logic, (ii) probabilistic assertions, and (iii) limited use of nominals. We start with our recently proposed logic crALC, where any ontology can be translated into a relational Bayesian ..."
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Abstract. This paper proposes a probabilistic description logic that combines (i) constructs of the wellknown ALC logic, (ii) probabilistic assertions, and (iii) limited use of nominals. We start with our recently proposed logic crALC, where any ontology can be translated into a relational Bayesian network with partially specified probabilities. We then add nominals to restrictions, while keeping crALC’s interpretationbased semantics. We discuss the clash between a domainbased semantics for nominals and an interpretationbased semantics for queries, keeping the latter semantics throughout. We show how inference can be conducted in crALC and present examples with real ontologies that display the level of scalability of our proposals. Key words: ALC logic, nominals, Bayesian/credal networks. 1
Probabilistic Graphical Models Probabilistic Graphical Models
"... Abstract This report 1 presents probabilistic graphical models that are based on imprecise probabilities using a comprehensive language. In particular, the discussion is focused on credal networks and discrete domains. It describes the building blocks of credal networks, algorithms to perform infer ..."
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Abstract This report 1 presents probabilistic graphical models that are based on imprecise probabilities using a comprehensive language. In particular, the discussion is focused on credal networks and discrete domains. It describes the building blocks of credal networks, algorithms to perform inference, and discusses on complexity results and related work. The goal is to present an easytofollow introduction to the topic.
Lower Bound Bayesian Networks – An Efficient Inference of Lower Bounds on Probability Distributions in Bayesian Networks
"... We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can use any available algorithms and tools for Bayesian networks i ..."
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We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can use any available algorithms and tools for Bayesian networks in order to represent and infer lower bounds. This new method yields results that are provable exact for trees with binary variables, and results which are competitive to existing approximations in credal networks for all other network structures. Our method is not limited to a specific kind of network structure. Basically, it is also not restricted to a specific kind of inference, but we restrict our analysis to prognostic inference in this article. The computational complexity is superior to that of other existing approaches. 1
GL2U: A Python Implementation for Approximate Inference on Credal Nets using Generic Loopy 2U
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EGL2U: Tractable Inference on Large Scale Credal Networks
, 2008
"... Credal networks [1, 2] generalize Bayesian networks [3] by associating with variables (closed convex) sets of conditional probability mass functions, i.e., credal sets 1, in place of precise conditional probability distributions. Credal networks are models of imprecise probabilities [4], which allow ..."
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Credal networks [1, 2] generalize Bayesian networks [3] by associating with variables (closed convex) sets of conditional probability mass functions, i.e., credal sets 1, in place of precise conditional probability distributions. Credal networks are models of imprecise probabilities [4], which allow the capturing