Bayesian Networks

THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks
Probabilistic Graphical Modeling
•
Applied mathematics,
•
uncertainity and complexity
Vilem Berka, [email protected]
Czech Technical University Prague, Montan Universitaet Leoben, 2006
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks – Definition
(Wikipedia)
A Bayesian network is a representation of the joint distribution over all
the variables represented by nodes in the graph.
Let the variables be X(1), ..., X(n).
Let parents(A) be the parents of the node A.
Then the joint distribution for X(1) through X(n) is represented as the
product of the probability distributions for i = 1 to n.
If X has no parents, its probability distribution is said to be unconditional,
otherwise it is conditional.
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks
(st-andrews.ac.uk)
Node – Edges graph types
[email protected]
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks
(st-andrews.ac.uk)
Graphical representation of a joint probability distribution,
representing dependence and conditional independence
relationships.
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks
(st-andrews.ac.uk)
Limitation of the BN - equivalence class (Functional networks)
Dynamic Bayesian networks (DBNs) – Functional loop over time.
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks
(st-andrews.ac.uk)
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks - Example
(Kevin Murphy)
University of British Columbia
[email protected]
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks – Applications
Medical diagnostics and probability estimations
Bayesian LAB – knowledge modeling, data mining
Market simulator
Network diagnostic and Repair
Automatic speech recognition engines
Decision making AI gaming SW
Microsoft:
Intelligent user interfaces. Office Assistant since version 97.
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Computer models in use
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Simulation model
Simulation run
Interpretation
Real world
Abstraction, modeling
Evaluation
Results
Experiment
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks
(BayesiaLAB)
Download the Tutorial at:
http://www.bayesia.com/GB/produits/bLab/BLabTour/BLabTour.php
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Networks
5 reasons to use
• Brainstorming, communication
• Probabilistic relations with
significant impact
• Understanding the data
• Ability to test What-if scenarios
• Similarity rules applications
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Bayesian Network editors
• Bayesia LAB trialware
• Microsoft Research
Download at:
http://research.microsoft.com/adapt/MSBNx
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka
THE RENEWABLE ENERGY RESOURCES – EUREGIO PROJECT
Microsoft research – Bayesian evaluation
Demonstration – automotive example
Vilem Berka, CTU Prague – Montan Universitaet Leoben
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© Vilem Berka