Bayesian Networks - Computational Intelligence

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Nov 7, 2013 (4 years ago)

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RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks1
BayesianNetworks
Prof.Dr.RudolfKruse,
PascalHeld
ComputationalIntelligenceGroup
DepartmentofKnowledgeProcessingandLanguageEngineering
FacultyofComputerScience
kruse@iws.cs.uni-magdeburg.de
Booksaboutthecourse
RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks8
http://www.computational-intelligence.eu/
KnowledgeBasedSystems
RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks9
HumanExpert
Ahumanexpertisaspecialistforaspecificdifferentiatedapplicationfieldwho
createssolutionstocustomerproblemsinthisrespectivefieldandsupportsthem
byapplyingthesesolutions.
Requirements

Formulatepreciseproblemscenariosfromcustomerinquiries

Findcorrectandcompletesolution

Understandableanswers

Explanationofsolution

Supportthedeploymentofsolution
KnowledgeBasedSystems(2)
RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks10
“Intelligent”System
Anintelligentsystemisaprogramthatmodelsthe
knowledgeandinferencemethodsofahumanexpert
ofaspecificfieldofapplication.
Requirementsforconstruction:

KnowledgeRepresentation

KnowledgeAcquisition

KnowledgeModification
QualitiesofKnowledge
RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks11
Inmostcasesourknowledgeaboutthepresentworldis
incomplete/missing(knowledgeisnotcomprehensive)

e.g.“Idon’tknowthebusdeparturetimesforpublicholidaysbecauseIonly
takethebusonworkingdays.”
vague/fuzzy/imprecise(knowledgeisnotexact)

e.g.“Thebusdepartsroughlyeveryfullhour.”
uncertain(knowledgeisunreliable)

e.g.“Thebusdepartsprobablyat12o’clock.”
Wehavetodecidenonetheless!
ReasoningunderVagueness
ReasoningwithProbabilities
...andCost/Benefit
Example
RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks12
Objective:Beattheuniversityat9:15toattendalecture.
Thereareseveralplanstoreachthisgoal:

P
1
:Getupat8:00,leaveat8:55,takethebusat9:00...

P
2
:Getupat7:30,leaveat8:25,takethebusat8:30...

...
Allplansarecorrect,but

theyimplydifferentcostsanddifferentprobabilities
toactuallyreachthatgoal.

P
2
wouldbetheplanofchoiceasthelectureisimportant
andthesuccessrateofP
1
isonlyabout80–95%.
Question:Isacomputercapableofsolvingthese
problemsinvolvinguncertainty?
UncertaintyandFacts
RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks13
Example:
Wewouldliketosupportarobot’slocalizationbyfixedlandmarks.
Fromthepresenceofalandmarkwemayinferthelocation.
Problem:
Sensorsareimprecise!

Wecannotconcludedefinitelyalocationsimplybecause
therewasalandmarkdetectedbythesensors.

Thesameholdstrueforundetectedlandmarks.

Onlyprobabilitiesarebeingincreasedordecreased.
DegreesofBelief
RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks14
We(orotheragents)areonlybelievingfactsorrulestosomeextent.
Onepossibilitytoexpressthispartialbeliefisbyusingprobabilitytheory.
“Theagentbelievesthesensorinformationto0.9”means:
In9outof10casestheagenttrustsinthecorrectnessofthesensoroutput.
Probabilitiesgatherthe“uncertainty”thatoriginatesduetoignorance.
Probabilities6=Vagueness/Fuzziness!

Thepredicate“large”isfuzzywhereas“ThismightbePeter’swatch.”
isuncertain.
RationalDecisionsunderUncertainty
RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks15
Choiceofseveralactionsorplans
Thesemayleadtodifferentresultswithdifferentprobabilities.
Theactionscausedifferent(possiblysubjective)costs.
Theresultsyielddifferent(possiblysubjective)benefits.
Itwouldberationaltochoosethatactionthatyieldsthelargesttotalbenefit.
DecisionTheory=UtilityTheory+ProbabilityTheory
Decision-theoreticAgent
RudolfKruse,MatthiasSteinbrecher,PascalHeldBayesianNetworks16
inputperception
outputaction
1:K←asetofprobabilisticbeliefsaboutthestateoftheworld
2:calculateupdatedprobabilitiesforcurrentstatebasedonavailableevidenceinclud-
ingcurrentperceptandpreviousaction
3:calculateoutcomeprobabilitiesforactions,givenactiondescriptionsandprobabil-
itiesofcurrentstates
4:selectactionAwithhighestexpectedutilitygivenprobabilitiesofoutcomesand
utilityinformation
5:returnA
DecisionTheory:Anagentisrationalifandonlyifitchooses
theactionyieldingthelargestutilityaveraged
overallpossibleoutcomesofallactions.