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

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.

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 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

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