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(COMP327)midterm01F.pdf
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COMP527:PatternRecognition
Fall2001
MidtermExamination
6November2001,9:00{10:20am
StudentName:
StudentNumber:
Instructions
1.Checkthatyouhaveall6pages(includingthiscoverpage). 2.Writeyournameandstudentnumberonthispage. 3.Answerallquestionsinthespaceprovided.Roughworkshouldbedoneonthebackpages. 4.Makeyouranswersasconciseaspossible.
Question1(10%): Question2(10%): Question3(18%): Question4(22%): Question5(15%): Question6(25%):
TOTAL(100%): \Theobjectiveofclassi.ertrainingistominimizetheclassi.cationerrorofthetraining set."Isthisstatementcorrect.Explainwhyorwhynot.
2.(10%)
\Themajordi.erencebetweenMAPestimationandMLestimationisthattheprior
parameterdistributionisincorporatedintheformerbutnotthelatter."Isthisstatement
correct.Explainwhyorwhynot.
Consideraclassi.cationproblemwiththreeclasseswhere11.0,12.1,13.1, 21.2,22.0,23.2,31.4,32.4,33.0.
(a)ComputetheconditionalrisksR(ijx)1.i.3,intermsoftheposteriorprobabil-ities.
(b)Givetheminimum-riskclassi.cationruleintermsoftheposteriorprobabilities.Use therejectoptionincaseofatieintheminimumrisk.
(b)WhenonlylimitedtrainingdataareavailableforbuildingaBayesianclassi.erbased onthenonparametricdensityestimationapproach,theclassi.cationerrormaybe ratherlargeeventhoughtheparametricapproachcangivemuchsmallererror.(You mighthaveobservedthisphenomenoninthe.rstassignment.)Explainwhythis couldhappen.
x1 x2 t
2 1 0
3 2 0
4 4 0
1 1 1
3 5 1

Provethattheyarelinearlyseparablebyprovidingalineardiscriminantfunctionforthe classi.cationtask.

P
exp(h wkjyj)
j.0
yk.PPh
c
k0.1exp(wk0jyj)
j.0
withthesamenotationalconventionasinthenotes. Usinggradient-descentasinthestandardback-propagationlearningalgorithm,showthat theper-epochupdatingruleforthehidden-to-outputweightscanbeexpressedasfollows:
n
X
(p)(p)(p)(p)(p)(p)(p)
.wkj.ywhere.(t;y)(1;y)y
kj kkkkk p.1
***THEEND***
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