Object- Oriented Bayesian Networks : An Overview

Object- Oriented Bayesian
Networks : An Overview
Presented By: Asma Sanam Larik
Course: Probabilistic Reasoning
Limitations of BN
Standard BN representation makes
it hard to
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
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
Our goal ?
Our goal is a more expressive
representation language with
◦ rigorous probabilistic semantics;
◦ model-based;
◦ supports hierarchical structure &
◦ exploits structure for effective
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
• 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
Reference : F.V.Jensen , T.D.Nelson “Bayesian Networks and Decision Graphs ”,
vol. 2, Springer 2007
An OOBN models a domain with
hierarchical structure & redundancy
An OOBN consists of a set of
◦ 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
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
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
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
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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