Object- Oriented Bayesian Networks : An Overview

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Object- Oriented Bayesian
Networks : An Overview
Presented By: Asma Sanam Larik
Course: Probabilistic Reasoning
Limitations of BN
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Standard BN representation makes
it hard to
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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:
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◦ highway traffic;
◦ military situation assessment.
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Control intelligent agents in
complex environments:
◦ Smart robot;
◦ intelligent building.
Problem : Knowledge Engineering

Main reuse mechanism: cut & paste
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How is the model updated?
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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:
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Proposed by Laskey Network fragments
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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 ?
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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
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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

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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
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Convert OOBN to MSBN and apply MSBN
inference approach
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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
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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

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