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Object- Oriented Bayesian Networks : An Overview

Object- Oriented Bayesian Networks : An Overview

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Object- Oriented Bayesian Networks : An Overview

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  1. Object- Oriented Bayesian Networks : An Overview Presented By: Asma SanamLarik Course: Probabilistic Reasoning

  2. Limitations of BN • Standard BN representation makes it hard to • construct • update • reuse • learn • reason with complex models.

  3. Scaling up • Our goal is to scale BNs to more complex domains • Large-scale diagnosis. • Monitor complex processes: • highway traffic; • military situation assessment. • Control intelligent agents in complex environments: • Smart robot; • intelligent building.

  4. Problem : Knowledge Engineering • Main reuse mechanism: cut & paste • How is the model updated? • How do we construct large BNs?

  5. Problem: BN Inference • BN Inference can be exponential • Inference complexity depends on subtle properties of BN structure. =>Will a large BN support efficient inference?

  6. Approach 1: • Proposed by Laskey Network fragments • A Network fragment is basically a set of related variable together with knowledge about the probabilistic relationships among the variables. • Two types of object were identified Input and Result fragments. Input fragments are composed together to form a result fragment. To join input fragments together an influence combinationruleis needed to compute local probability

  7. Exploit structure!The architecture of complexity [Herbert Simon, 1962] • many complex systems have a nearly decomposable, hierarchic structure. • Hierarchic systems are usually composed of only a few different kinds of subsystems. • By appropriate “recoding”, the redundancy that is present but unobvious in the structure of a complex system can often be made patent.

  8. Our goal ? • Our goal is a more expressive representation language with • rigorous probabilistic semantics; • model-based; • supports hierarchical structure & redundancy; • exploits structure for effective inference!

  9. Object-Oriented Bayesian Network • Classes represent types of object – Attributes for a class are represented as OOBN nodes – Input nodes refer to instances of another class – Output nodes can be referred to by other classes – Encapsulated nodes are private » Conditionally independent of other objects given input and output nodes • Classes may have subclasses – Subclass inherits attributes from superclass – Subclass may have additional attributes not in superclass • Classes may be instantiated – Instances represent particular members of the class

  10. Example Reference :F.V.Jensen , T.D.Nelson “Bayesian Networks and Decision Graphs ”, vol. 2, Springer 2007

  11. OOBN • An OOBN models a domain with hierarchical structure & redundancy • An OOBN consists of a set of objects: • simple objects: random variables • complex objects :have attributes which are enclosed objects.

  12. Inter Object Interaction • Related objects can influence each other via imports and exports. • X imports A from Y => • value of X can depend on the value of A. • objects related to X can import A from X.

  13. Imports and Exports / Inputs and Output Variables • Value of object depends probabilistically on the value of its imports • A simple object is associated with a conditional probability table • distribution over its values given values for its imports. • The value of a complex object X is composed of the values for its attributes • Its probabilistic model is defined recursively from the models of its attributes

  14. Semantics • Theorem: The probabilistic model for an object X defines a conditional probability distribution • P( value of X | imports into X from enclosing object)

  15. Old Mac Donald Case Study Reference: O. Bangsø and P.-H. Wuillemin. “Top-down construction and repetitive structures representation in Bayesian networks”. Proceedings of the 13th International Florida Artificial Intelligene Research Society Conference (FLAIRS-2000), pp. 282–286, AAAI Press, 2000

  16. Sub Classing and Inheritance • If a class C’ should be a subclass of C it should hold • the set of input variables for C is a subset of input variables for C’ • the set of output variables for C is a subset of output variables for C’

  17. Reference: F.V.Jensen, T.D.Nelson “Bayesian Networks and Decision Graphs ” ,vol. 2, Springer 2007

  18. OOBN Inference • The OOBN representation allows us to easily construct large complex models • Can we do inference in these models? • BN constructed very large… efficient inference?

  19. Approaches to Inferencing • Convert to normal BN and use standard inference techniques • Convert OOBN to MSBN and apply MSBN inference approach • By exploiting the modularity we can obtain good results • Algorithms are being developed in this area

  20. Conclusion • In essence, where Bayesian networks contain two types of knowledge relevance relationships and conditional probabilities OOBNs contain a third type of knowledge organizational structure. • They can model static situations but cannot model situations where instances are changing

  21. References • D.Koller and A.Pfeffer. “Object Oriented Bayesian Networks” .Proceedings of the Thirteenth Annual Conference on Uncertainty in Artificial Intelligence. August 1-3, 1997, Brown University, Providence, Rhode Island, USA. Morgan Kaufman Publishers Inc, San Francisco, 1997. • K. B. Laskey and S. M. Mahoney “Network Fragments: Representing Knowledge for Constructing Probabilistic Models”. Proceedings of Thirteenth Annual Conference on uncertainty in Artificial Intelligence. Morgan Kaufman Publishers Inc., San Francisco, 1997. • O. Bangsø and P.-H. Wuillemin. “Top-down construction and repetitive structures representation in Bayesian networks”. Proceedings of the 13th International Florida Artificial Intelligene Research Society Conference (FLAIRS-2000), pp. 282–286, AAAI Press, 2000. • M. Fenton, Nielsen, L. M. (2000). Building Large-Scale Bayesian Networks,The Knowledge Engineering Review 15(3): 257–284. • J.Pearl(1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Series in Representation and Reasoning, Morgan Kaufmann Publishers,San Mateo, CA. • M. Julia Gallego, “Bayesian networks inference: Advanced algorithms for triangulation and partial abduction”, Ph.D. dissertation, Departamento de SistemasInform´aticos, University of Castilla - La Mancha (UCLM), 2005 • U.B. Kjaerulff, A.L. Madsen, “Bayesian Networks and Influence Diagrams : A Guide to Construction and Analysis”, Springer 2008 ,pp. 91-98 • F.V.Jensen, T.D.Nelson “Bayesian Networks and Decision Graphs ”,vol. 2, Springer 2007, pp.84-91 • HuginTutorial, • H.Simon,"The Architecture of Complexity", Proceedings of American Philosophical Association, 1962