Object- Oriented Bayesian Networks : An Overview

Presented By: Asma Sanam Larik Course: Probabilistic Reasoning

Limitations of BN

 ◦ ◦

Standard BN representation makes it hard to

◦ construct ◦ update reuse learn ◦ reason with complex models.

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.

Problem : Knowledge Engineering

 Main reuse mechanism: cut & paste  How is the model updated?

 How do we construct large BNs?

Problem: BN Inference

  BN Inference can be exponential

Inference complexity depends on subtle properties of BN structure.

=>Will a large BN support efficient inference?

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 combination rule is needed to compute local probability

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.

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!

Object-Oriented Bayesian Network

Classes represent types of objectAttributes for a class are represented as OOBN nodesInput nodes refer to instances of another classOutput nodes can be referred to by other classesEncapsulated nodes are private » Conditionally independent of other objects given input and

output nodes

Classes may have subclassesSubclass inherits attributes from superclassSubclass may have additional attributes not in superclassClasses may be instantiatedInstances represent particular members of the class

Example

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

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.

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.

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

Semantics

Theorem: The probabilistic model for an object X defines a conditional probability distribution

P( value of X | imports into X from enclosing object)

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

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’

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

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?

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

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

         

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 Sistemas Inform´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 Hugin Tutorial, www.hugin.com/developer/tutorials/OOBN H.Simon,"The Architecture of Complexity", Proceedings of American Philosophical Association, 1962