Transcript Predictive and Contextual Feature Separation for Bayesian

Contextual level
Predictive level
Predictive and Contextual Feature
Separation for Bayesian Metanetworks
Vagan Terziyan
[email protected]
Industrial Ontologies Group, University of Jyväskylä, Finland
KES-2007, Vietri sul Mare , Italy
12 September 2007
Session IS03: Context-Aware
Adaptable Systems and Their
Applications (17:10, room D)
Contents
 Bayesian Metanetworks


Metanetworks for
managing conditional
dependencies
Metanetworks for
managing feature
relevance
 Feature Separation for
Bayesian Metanetworks
 Conclusions
Vagan Terziyan
Industrial Ontologies Group
Department of Mathematical
Information Technologies
University of Jyvaskyla (Finland)
http://www.cs.jyu.fi/ai/vagan
This presentation: http://www.cs.jyu.fi/ai/KES-2007.ppt
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Conditional dependence between
variables X and Y
Random variable X {x1, x2, …, xn}
Fixed conditional probability table:
P(Y|X)
y1
y2
P(X)
X
…ym
x1
p(x1| y1)
p(x1| y2)
p(x1| ym)
x2
p(x2| y1)
p(x2| y2)
p(x2| ym)
… xn
p(xn| y1)
p(xn| y2)
… p(xn| ym)
P(Y|X)
Y
P(Y)
Random variable Y {y1, y2, …, ym}
P(Y) = X (P(X) · P(Y|X))
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Bayesian Metanetwork
 Definition. The Bayesian Metanetwork is a
set of Bayesian networks, which are put on
each other in such a way that the elements
(nodes or conditional dependencies) of every
previous probabilistic network depend on the
local probability distributions associated with
the nodes of the next level network.
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Two-level Bayesian C-Metanetwork
for Managing Conditional Dependencies
Contextual level
Predictive level
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Two-level Bayesian C-Metanetwork
for managing conditional dependencies
Contextual level
P(B|A)
P(Y|X)
A
B
X
Predictive level
Y
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Two-level Bayesian R-Metanetwork
for Modelling Relevant Features’ Selection
Contextual level
Predictive level
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Feature relevance modelling
We consider relevance as a
probability of importance of
the variable to the inference
of target attribute in the
given context. In such
definition relevance inherits
all properties of a probability.
P(X)
X
Probability to have this model
is:
Probability to have this
model is:
P((X)=”no”)= 1-X
P((X)=”yes”)=  X
P0(Y)
P(Y|X)
Y
Y
P1(Y)
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General Case of Managing Relevance
Probability
P(XN)
P(Y ) 
1
N
 nxs
s 1
  ... [ P(Y | X 1, X 2,... XN ) 
X1 X 2
XN
nxr 


r ( ( Xr )" yes ")
Xr
 P( Xr ) 
(1  


Xq
)]
q ( ( Xq )"no")
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Example of Relevance Bayesian
Metanetwork
Conditional
relevance !!!
1
P(Y ) 
  {P(Y | X )  [nx  P( X ) 
nx X
  P( X |  A )  P( A )  (1   X )]}.
A
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Example of Relevance Bayesian
Metanetwork
Ψ(A)
Ψ(X)
Ψ(B)
Contextual level
Ψ(Y)
Predictive level
A
B
X
Y
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Separation of contextual and
predictive attributes is based on:
 Part_of context
 Role-based context
 Interface-based context
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The nature of part_of context
air pressure
dust
humidity
temperature
Machine
emission
Environment
Sensors
X
x1
x2
x3
predictive attributes
x4
x5
x6
x7
contextual attributes
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Context Description Framework
(CDF) Basic Data Model
Khriyenko O., Terziyan V., A Framework for Context-Sensitive Metadata
Description, In: International Journal of Metadata, Semantics and Ontologies,
Inderscience Publishers, ISSN 1744-2621, 2006, Vol. 1, No. 2, pp. 154-164.
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Part-of Context in CDF
part_of
Resource i
Property_q
Property_n
Resource k
Value_r
Property_p
Value_m
Value_s
RDF container
Context_h
RDF statement
true_in_context
Resource_k
Property_n
Predictive feature
Resource_i
Property_q Value_m
Resource_i
Property_p
Value_r
Contextual features
Value_s
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Multiple Context Inheritance …
Golf_Club
part_of
located_in
Paris
members_amount
has_age
John
48 y.
located_in
part_of
Resource
John
Symphonic_Orchestra
Predictive
features
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belongs_to
Bagnolet
State
Contextual Features (inherited from both parents)
environment_1_location
environment_1_members amount
environment_2_location
environment_2_belongs_to
age
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Role-based context
The example of the
proactive object (human
resource), which is
member of several
organization and which is
playing different roles in
each of them. The context
of this object should
include the description of
these roles (duties,
commitments,
responsibilities, etc).
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Interface-based context
a
b
The example of the domain object
(aircraft) is shown in different interfaces:
(a) Google Maps; (b) pilots’ control panel;
(c) manufacturing design e-manual. Each
interface is considered as a context,
which affect on which parameters of the
aircraft are to be shown
c
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Summary
 We are considering a context as a set of contextual
attributes, which are not directly effect probability
distribution of the target attributes, but they effect on a
“relevance” of the predictive attributes towards target
attributes.
 Bayesian Metanetwork allows modelling such contextsensitive feature relevance. The model assumes that the
relevance of predictive attributes in a Bayesian network
might be a random attribute itself and it provides a tool to
reason based not only on probabilities of predictive
attributes but also on their relevancies.
 For Bayesian Metanetwork there is a need to distinguish
predictive and contextual attributes and in this paper the
separation of attributes is described based on three
notions of a context: part_of context, role-based context
and interface-based context.
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Read more about Bayesian
Metanetworks in:
Terziyan V., A Bayesian Metanetwork, In: International
Journal on Artificial Intelligence Tools, Vol. 14, No. 3, 2005,
World Scientific, pp. 371-384.
http://www.cs.jyu.fi/ai/papers/IJAIT-2005.pdf
Terziyan V., Vitko O., Bayesian Metanetwork for
Modelling User Preferences in Mobile Environment, In:
German Conference on Artificial Intelligence (KI-2003),
LNAI, Vol. 2821, 2003, pp.370-384.
http://www.cs.jyu.fi/ai/papers/KI-2003.pdf
Terziyan V., Vitko O., Learning Bayesian Metanetworks from
Data with Multilevel Uncertainty, In: M. Bramer and V. Devedzic
(eds.), Proceedings of the First International Conference on
Artificial Intelligence and Innovations, Toulouse, France, August 2227, 2004, Kluwer Academic Publishers, pp. 187-196 .
http://www.cs.jyu.fi/ai/papers/AIAI-2004.ps
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