Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Descision theory with Bayesian Networks
Margus Niitsoo,Aivo J¨urgenson
April 22,2009
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Outline
1
Model of descision theory
2
Descision trees and computing them
3
Inﬂuence diagram for one descision
4
Inﬂuence diagrams in general
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Utility
We associate numbers with diﬀerent states of the world
Better states get higher numbers
That number is called the Utility
The theory is that maximal expected utility is most desirable.
Some situations are hard to model
For instance  Avoiding a disaster
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Where do we get utilities
Out of thin air
Something objective (money,grades)
The gamblers way!
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Axioms of two true Gamblers
The axioms of rational choice by Neumann and Morgenstern:
Let A,B,C,D be diﬀerent distributions of world outcomes
(lotteries).Assume we have a partial ordering ≥ on all possible
outcome distributions that satisﬁes
Reﬂexivity,Completeness,Transitivity
Preference increasing:pA+(1 −p)B ≥ qA+(1 −q)B iﬀ
p ≥ q
Continuity:A ≥ B ≥ C means there exists a q such that
B ≡ pA+(1 −p)B.
Independence:C = pA+(1 −p)B and C ≡ D imply
D ≡ pA+(1 −p)B
If the set of atoms is ﬁnite,this guarantees a utility function exists.
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Descision trees
Parts
Descision nodes
Chance nodes
Utility leaves
History is known!
Exponential growth
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Descision trees
Parts
Descision nodes
Chance nodes
Utility leaves
History is known!
Exponential growth
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Descision trees
Parts
Descision nodes
Chance nodes
Utility leaves
History is known!
Exponential growth
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Descision trees
Using Bayesian Networks
Solution concept  Strategy
Calculating the tree
Coalescing
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Inﬂuence diagrams
Get rid of the tree
Introduce extra nodes to BN
Calculate!
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
In general
Descisions aﬀect one another
Descision sequence ﬁxed!
No Forgetting!
Partitions whole BN into sets
The concept of a solution  Policy
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
In general
Descisions aﬀect one another
Descision sequence ﬁxed!
No Forgetting!
Partitions whole BN into sets
The concept of a solution  Policy
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
In general
Descisions aﬀect one another
Descision sequence ﬁxed!
No Forgetting!
Partitions whole BN into sets
The concept of a solution  Policy
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
In general
Descisions aﬀect one another
Descision sequence ﬁxed!
No Forgetting!
Partitions whole BN into sets
The concept of a solution  Policy
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
Model of descision theory
Descision trees and computing them
Inﬂuence diagram for one descision
Inﬂuence diagrams in general
Questions anyone?
Aivo will continue next week with generalizations
Margus Niitsoo,Aivo J¨urgenson
Descision theory with Bayesian Networks
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