Mappe concettuali Supervised Statistical Learning

APr (Y / ✗ )) Th WHEREXo °== = FeckolTe✓ > Fh .probabili( ofobservingXo) fromPOSTERIOR PROBABKITY hty Xo if populationitLIKELIHOOD comesbelongings hof Populationto observed Xogiven havewe . Bayes → possibleLowestrateEXAMPLE error-1> mozzate✓ hpr hl✗✗ ( )At Y Xoit EQUALTO✗ 1- =is ma✗= =o Bayesbecame alwaysFierclassithe Will BayesChoose the Theprobabiliclass Overall bygivenwhich isfor ty reteerrorthebelongingsOF Largestis .. )( Pr HIX)(YE1- ✗una =where thethe probabiliexpectations average tyspossibleall XValues ofover .Ho data classificaConditionat that'sdistributionreal X toImpossiblethewith BayesY Computewhyany theUnknownis isofWever given usu, , È consideri standardgoldouras Modelsherwhichagainst atto compare .Mary highéstestiueedConditionat andtry to classi fy classapproaches distribution to theObservation withthenstimate probthe givenae .CONFUSION MATRIX( Problemsbinaryin Classification ) PREDKTED CLASS WHERE :i Yes No Tot betelTP

TP stands for True Positive

FP stands for False Positive

TN stands for True Negative

FN stands for False Negative

ACCURACY = (TP + TN) / (TP + FP + TN + FN)

ERROR RATE = 1 - ACCURACY

MISCLASSIFICATION ERROR = (FP + FN) / (TP + FP + TN + FN)

SENSITIVITY or RECALL = TP / (TP + FN)

SPECIFICITY = TN / (TN + FP)

PRECISION = TP / (TP + FP)

F1 SCORE = 2 * (PRECISION * RECALL) / (PRECISION + RECALL)

✗nearor : ✗, precision + recall

In Logistic functionthe Logisticregressioni we Use, pcxt-e.FI??-> The valueLogistic XofShaped regaroklessfunction S thewiu produce curve wiuan weso- , ,Sensible [obtain between and 13prediction 0a .The Logistic modelg.pt#=eBotB" Non by boththefaking log Sides getweon a, PotràlogKaos =valuecantare anybe andTween A0 LOGODDS LOGITORE )" In ✗Logistic regressioni bySingIncreaLOGISTIC regressioni LOOT THATAHASIn oddsexample value ,doseof the very toour , LINEARIS IN Xand probabilihighandindicate veryvery0 ty0 lowof disceseCoronari heart odds B1bythe logunit Changone es. - ,✓ oddsHowever byequivalentirelationship themultiplithesince or esy, EB~ ?( XI and Xbetweenp notis aThe pcxlchanges linestraight Bathatcorrispondadueamount notdasto , )PCXchanganiudepend to in✗ associatedunit withtheinIncreaseore a- ✗the Howevalue unitof Increase inX veriCurrent oneon -.Baif ✗ puttheis →Singincircapositive SingIncrean, ✗B1 the

)decreasingpcx→Singincircaif negativeis n,✓Band pa be fondcanthrough estimatoriML . f-YiMicaEd( BoLikelihood (function binary IlPC PCXilL 'pcxi pcxi✗ 1-:case =on = -, , ,the andof BiBoestimato thisChosen functionmaxiMizetoare .PROFESSOR NOTES :To }{P BoBy considerinoderivativo(ihoodthe Be andmaxiMize log Vectorset thatlike the to ofqual includeXithewe inputs0 assuueing=e s- . ,the accomodateterneConstant intercepttheto1 writewe can :,fin2ITL BY( linear potwopcxi equationYi → in= nono= ;- -2ps' Ii ÌaNB E expected)first of specificThe pXi PCXIFirst thatthe equationComponent class thethe numberYi of1 matchesis so score s 1 = es; := on,. observed number RaphsonNewtonThe problem sdvedbe algoritmithroughcan . LPr GH'ÉÈ valueERROR ThisEXAMPLE model probabili Tobaccopredictsthe cholz ty of using-.%>Intercept 11894 8.55731390 00 0000-- ..tobacco 1453 0248 586600 000000 .. " B1✓ associatedA unit in tobacco isIncreaseore -with in the

modeluntilthe Significant fromalonethe several times further be theis termsre: no can .. excluderenewedmodel decide VariabledeviWAY Fit Variable ofSECOND and then form whichthe toi of with analysis tore each anceperare an .(LogRESI 2OF MODELFIITEDDEUIANCE ADUAL : -difference their residua1 deviIndividualofMODELSDEVIANCEBETWEEN TWO ances: .Linear discrimina analysisntParametri dmodel when nellstimate ogisticfor classesstableregressioni separatethe two areveryise s un IOVERMORE that's whywe LDAUseLdoesn't stablerequire alsoLDA SmailLDAnormali whcnty is ismore n. distribution predictusand the ✗of is< inapproxiueately classnormal each .isLDA whenvery popularhavewe twonon+morerespon classesses .The Fisherbasic ueethodWhat Written We hadbove by IBasicallyFisher neededBasic Fcawas to /andStep meth tuo ofclassesthestep 001isa ✗explorationa arrestiof matewe compare.thresholdwith andthresholdand classvalue had otherwisetheObject toclass thanestito classify thethen mate grate

1. ifI is oa toanwe ✗ . L< relatedconsideraWeFGIX Allthatthink MeedIf ) monotoniaisto canwe nywe mountainIncrease the TransformationorderUymonotonia Proper )s party of il(pro ✗f-of< .in the functiondirection rSpaceXsone ,WhyThat is distanceUsewe thethen fromOrigintw din✗ Measureand it thatcomparet direction dowithwith the thresholdNon .weneedto .Fino goodea stimatefor the direction Fora directionofw given separabilithe tyw ,. >( beTween defineis dassamples 't tdkes faceno of theWIE accountIo/ 7Wtf wtxo=- that- Xj, Will have differentiiiygenera> ObviousOne approach variancesWould be Distance orcovariancesbetweento >Choose Measurementbethlenthat direction classesdong is sWhich tothe sommarituo .theclasses samplesseare BYhost their Mears and