Multi-entity bayesian networks without multi-tears

2005

Possibilistic logic and Bayesian networks have provided advantageous methodologies and techniques for computerbased knowledge representation. This paper proposes a framework that combines these two disciplines to exploit their own advantages in uncertain and imprecise knowledge representation problems. The framework proposed is a possibilistic logic based one in which Bayesian nodes and their properties are represented by local necessity-valued knowledge base. Data in properties are interpreted as set of valuated formulas. In our contribution possibilistic Bayesian networks have a qualitative part and a quantitative part, represented by local knowledge bases. The general idea is to study how a fusion of these two formalisms would permit representing compact way to solve efficiently problems for knowledge representation. We show how to apply possibility and necessity measures to the problem of knowledge representation with large scale data.

Possibilistic logic and Bayesian networks have provided advantageous methodologies and techniques for computerbased knowledge representation. This paper proposes a framework that combines these two disciplines to exploit their own advantages in uncertain and imprecise knowledge representation problems. The framework proposed is a possibilistic logic based one in which Bayesian nodes and their properties are represented by local necessity-valued knowledge base. Data in properties are interpreted as set of valuated formulas. In our contribution possibilistic Bayesian networks have a qualitative part and a quantitative part, represented by local knowledge bases. The general idea is to study how a fusion of these two formalisms would permit representing compact way to solve efficiently problems for knowledge representation. We show how to apply possibility and necessity measures to the problem of knowledge representation with large scale data.

In most current applications of belief networks, domain knowledge is represented by a single belief network that applies to all problem instances in the domain. In more complex domains, problem-specific models must be constructed from a knowledge base encoding probabilistic relationships in the domain. Most work in knowledge-based model construction takes the rule as the basic unit of knowledge. We present a knowledge representation framework that permits the knowledge base designer to specify knowledge in larger semantically meaningful units which we call network fragments. Our framework provides for representation of asymmetric independence and canonical intercausal interaction. We discuss the combination of network fragments to form problem-specific models to reason about particular problem instances. The framework is illustrated using examples from the domain of military situation awareness.

2003

During the past decades, many methods have been developed for the creation of Knowledge-Based Systems (KBS). For these methods, probabilistic networks have shown to be an important tool to work with probability-measured uncertainty. However, quality of probabilistic networks depends on a correct knowledge acquisition and modelation.

Lecture Notes in Computer Science, 2002

Interacting with huge conditional probability tables (i.e. variables with multiple states and multiple parents) in Bayesian belief networks (BBNs) makes it difficult for experts to create and employ probabilistic models. Although it is possible to learn the structure and conditional probabilities of Bayesian networks from existing data using a variety of algorithms, the role of human experts is still crucial to validate and to maintain such systems. Researchers have investigated the use of graphical interfaces and knowledge engineering techniques to support experts' interaction with complex BBNs. We propose a case-based approach to interact with conditional probability tables. This approach allows experts to define particular cases and focus their attention on them. By focussing on cases, rather than the whole conditional probability table (CPT), the intellectual burden on the expert is diminished, or at least divided into manageable pieces. Important cases defined by experts can be saved for further inspection and maintenance of CPTs. The advantages of this approach are evident when the network contains variables with multiple parents and special configurations of the network (i.e. variables with common parents). We developed a cased-based tool (cbCPT) especially designed to apply knowledge engineering principles to CPT navigation, elicitation, maintenance and evaluation. In addition, we report on a preliminary usability study that shows how users reacted to cbCPT and other available CPT tools.

Intelligent systems in an open world must reason about many interacting entities related to each other in diverse ways and having uncertain features and relationships. Traditional probabilistic languages lack the expressive power to handle relational domains. Classical first-order logic is sufficiently expressive, but lacks a coherent plausible reasoning capability. Recent years have seen the emergence of a variety of approaches to integrating first-order logic, probability, and machine learning. This paper presents Multi-entity Bayesian networks (MEBN), a formal system that integrates First Order Logic (FOL) with Bayesian probability theory. MEBN extends ordinary Bayesian networks to allow representation of graphical models with repeated sub-structures, and can express a probability distribution over models of any consistent, finitely axiomatizable first-order theory. We present the logic using an example inspired by the Paramount Series Star Trek.

Proceedings of the 19th International Conference on Enterprise Information Systems, 2017

Good representing and reasoning with uncertainty is a topic of growing interest within the community of artificial intelligence (AI). In this context, the Multi-Entity Bayesian Networks (MEBNs) are proposed as a candidate solution. It's a powerful tool based on the first order logic expressiveness. Furthermore, in the last decade they have shown its effectiveness in various complex and uncertainty-rich domains. However, in most cases the random variables are vague or imprecise by nature, to deal with this problem; we have to extend the standard Multi-Entity Bayesian Networks to improve their capabilities for good representing and reasoning with uncertainty. This paper details a promising solution based on fuzzy logic; it permits to overcome the weaknesses of classical Multi-Entity Bayesian networks. In addition, we have proposed a general process for the inference task. This process contains four steps, (1) Generating a Fuzzy Situation Specific Bayesian Networks, (2) Computing fuzzy evidence, (3) Adding virtual nodes, and (4) finally, the fuzzy probabilistic inference step. Our process is based on the virtual evidence method in order to incorporate the fuzzy evidence in probabilistic inference, moreover, approximate or exact algorithms can be used, and this choice of inference type depends to the contribution of the domain expert and the complexity of the problem. Illustrative examples taken from the literatures are considered to show potential applicability of our extended MEBN.

1990

We describe how to combine probabilistic logic and Bayesian networks to obtain a new framework (\Bayesian logic") for dealing with uncertainty and causal relationships in an expert system. Probabilistic logic, invented by Boole, is a technique for drawing inferences from uncertain propositions for which there are no independence assumptions. A Bayesian network is a \belief net" that can represent complex conditional independence assumptions. We show how to solve inference problems in Bayesian logic by applying Benders decomposition to a nonlinear programming formulation. We also show that the number of constraints grows only linearly with the problem size for a large class of networks.

Uncertainty in Artificial …, 2005

Intelligent systems in an open world must reason about many interacting entities related to each other in diverse ways and having uncertain features and relationships. Traditional probabilistic languages lack the expressive power to handle relational domains. Classical first-order logic is sufficiently expressive, but lacks a coherent plausible reasoning capability. Recent years have seen the emergence of a variety of approaches to integrating first-order logic, probability, and machine learning. This paper presents Multi-entity Bayesian networks (MEBN), a formal system that integrates First Order Logic (FOL) with Bayesian probability theory. MEBN extends ordinary Bayesian networks to allow representation of graphical models with repeated sub-structures, and can express a probability distribution over models of any consistent, finitely axiomatizable first-order theory. We present the logic using an example inspired by the Paramount Series Star Trek.

1989

Causal probabilistic networks have proved to be a useful knowledge representation tool for modelling domains where causal relations in a broad sense are a natural way of relating domain objects and where uncertainty is inherited in these relations. This paper outlines an implementation the HUGIN shell -for handling a domain model expressed by a causal probabilistic network. The only topological restriction imposed on the network is that, it must not contain any directed loops. The approach is illustrated step by step by solving a. genetic breeding problem. A graph representation of the domain model is interactively created by using instances of the basic network componentsnodes and arcs-as building blocks. This structure, together with the quantitative relations between nodes and their immediate causes expressed as conditional probabilities, are automatically transformed into a tree structure, a junction tree. Here a computationally efficient and conceptually simple algebra of Bayesian belief universes supports incorporation of new evidence, propagation of information, and calculation of revised beliefs in the states of the nodes in the network. Finally, as an exam ple of a real world application, MUN1N an expert system for electromyography is discussed.