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2019F-178-Mid

Bayes classifiers are probabilistic models based on Bayes' Theorem. They predict class membership by calculating the probability of a sample belonging to a class, assuming feature independence (as in Naive Bayes).

Mason Bennett
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CS178MidtermExamMachineLearningandDataMining:Fall2019MondayNovember4th,2019Yourname:Row/SeatNumber:YourID#(e.g.,123456789)UCINetID(e.g.ucinetid@uci.edu)«PleaseputyournameandIDoneverypage.«Totaltimeis50minutes.READTHEEXAMFIRSTandorganizeyourtime;don'tspendtoolongonanyoneproblem.«Pleasewriteclearlyandshowallyourwork.oIfyouneedclarificationonaproblem,pleaseraiseyourhandandwaitfortheinstructororTAtocomeover.Youmayuseonesheetcontaininghandwrittennotesforreference,anda(basic)calculator.Tuminyournotesandanyscratchpaperwithyourexam.Problems1BayesClassifiers,(10points.)32NearestNeighborRegression,(12points.)53Truo/False,(10points.)74SupportVectorMachines,(10points.)95VCDimensionality,(10points.)1Total,(52points.)

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BayesClassifiers,(10points.)I12Considerthetableofmeasureddatagivenatright.Wewillusethecblotwoobservedfeatures,,7,topredicttheclassy.Eachfeaturebbocantakeononeofthreevalues,x;€{a,b,c}.bc|0Tnthecaseofatie,wewillprefertopredictclassy=0.acll(1)WritedowntheprobabilitieslearnedbyanaiveBayesclassificr:(§points.)NNh—0-1aa1ply=0):ply=1):glcallpor=aly=0):on=aly=1)::per=bly=0):pn=bly=1):po=cly=0):pn=cly=1):prz=aly=0):pm=aly=1):Pra=bly=0):zy=bly=1):Pay=cly=0):ory=cly=1):(2)UsingyournaiveBayesmodel,whatvalueofywouldyoupredictgiven(x1=a,x2=b)?:(3points.)(3)UsingyournaiveBayesmodel,computetheprobabilities:(3points.)ply=01=bz2=c):py=11=br=c):
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