Motivation. We talk today for a more flexible approach for modeling the conditional probabilities.

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1 Baysia Ntworks

2 Motivatio Th coditioal idpdc assuptio ad by aïv Bays classifirs ay s too rigid spcially for classificatio probls i which th attributs ar sowhat corrlatd. W talk today for a or flibl approach for odlig th coditioal probabilitis. Baysia Ntwork Eplicitly odls th idpdc rlatioships i th data. Us ths idpdc rlatioships to ak probabilistic ifrcs. Also kow as: Blif Nt Bays Nt Causal Nt

3 Baysia tworks A sipl graphical otatio for coditioal idpdc assrtios. Syta: a st of ods o pr variabl attribut a dirctd acyclic graph lik as: "dirctly iflucs" a coditioal distributio for ach od giv its parts: X i arts X i Th coditioal distributio is rprstd as a coditioal probability tabl CT givig th distributio ovr X i for ach cobiatio of part valus.

4 Eapl rls apl I' at work ighbor Joh calls to say y alar is rigig but ighbor Mary dos't call. Sotis th alar is st off by ior arthquaks. Is thr a burglar? Joh always calls wh h hars th alar but sotis cofuss th tlpho rigig with th alar. Mary liks rathr loud usic ad sotis isss th alar. Variabls: Burglary Earthquak Alar JohCalls MaryCalls Ntwork topology rflcts "causal" kowldg: A burglar ca st th alar off A arthquak ca st th alar off Th alar ca caus Mary to call Th alar ca caus Joh to call

5 Eapl cot d To sav spac so of th probabilitis hav b oittd fro th diagra. Th oittd probabilitis ca b rcovrd by otig that X - X ad X Y - XY whr dots th opposit outco of. Th topology shows that burglary ad arthquaks dirctly affct th probability of alar but whthr Mary or Joh call dpds oly o th alar. Thus our assuptios ar that thy do t prciv ay burglaris dirctly ad thy do t cofr bfor callig.

6 Satics parts Suppos w hav th variabls X X. Th probability for th to hav th valus rspctivly is : : is short for X X.g. j a b j a a a b b i i i i i i parts...

7 Ifrc i Baysia Ntworks Th basic task for a probabilistic ifrc syst is to coput th postrior probability for a qury variabl class attribut giv so obsrvd vt that is so assigt of valus to a st of Notatio: vidc variabls othr attributs. X dots qury variabl E dots th st of vidc variabls E E ad is a particular vt i.. a assigt to th variabls i E. Y will dot th st of th raiig variabls hidd variabls. A typical qury asks for th postrior probability E.g. w could ask: What s th probability of a burglary if both Mary ad Joh call burglary johhcalls arycalls?

8 Classificatio Suppos w ar giv for th vidc variabls E E thir valus ad w wat to prdict whthr th qury variabl X has th valu or ot. For this w coput ad copar th followig: α α... Howvr how do w coput:... α ad α......? What about th hidd variabls Y Y k?

9 Ifrc by uratio Eapl: burglary johcalls arycalls? Abbrv. b j b a j a j b j b j b a a α α α b a j b a j b a j b a j a α ad y y k y y k k k y y y y α α α α I gral:

10 Nurically b j α a jab b j α a ja b b j α b a ja a ab α * b j α b a ja a a b α * B j α < > < >.

11 b j b j α a jaaabb α b a jaa ab α b a jaaab + ab α b jaa ab + ab + j a a ab + ab α *.00*.9*.7*.95* * *.0*.05* *.998 α *.00059

12 b j b j α b a jaa a b α b a jaaa b + a b α bjaa a b + a b + j a a a b + a b α *.999*.9*.7*.29* * *.0*.7* *.998 α *.005 α / b j * b j *

13 Costructig Baysia tworks. Choos a ordrig of variabls X X 2. For i to add X i to th twork slct parts fro X X i- such that X i artsx i X i X... X i- This choic of parts guarats: X X i X i X X i- chai rul i X i artsx i by costructio Choosig th parts fro X X i- is do by doai hua prts.

14 Th ordrig of variabls is vry iportat. E.g. suppos w choos th followig ordrig for M J A B E Addig MaryCalls : No parts Eapl Addig JohCalls: JM J? I othr words is Joh callig idpdt of Mary callig? Clarly ot sic o ay giv day if Mary calld th th probability that Joh calld is uch bttr tha th backgroud probability that h calld. So w add a lik fro MaryCalls to JohCalls.

15 Eapl W cotiu with th ordrig for M J A B E Addig th A Alar od: Is A J M A J? A J M A? No. Clarly if both call it s or likly that th alar has go off that if just o or ithr call so w d both MaryCalls ad JohCalls as parts.

16 Eapl W cotiu with th ordrig for M J A B E Addig B Burglary od: Is B A J M B A? B A J M B? Ys for th first. No for th scod. If w kow th alar stat th th call fro Joh or Mary ight giv us iforatio about th pho rigig or Mary s usic but ot about burglary. So w d just Alar as part.

17 W cotiu with th ordrig for M J A B E Addig E Earthquak od: Is E B A J M E A? E B A J M E A B? Eapl No for th first. Ys for th scod. If th alar is o it is or likly that thr has b a arthquak. But if w kow thr has b a burglary th that plais th alar ad th probability of a arthquak would b oly slightly abov oral. Hc w d both Alar ad Burglary as parts.

18 Eapl cot d So th twork is lss copact if w go o-causal: ubrs i CTs dd istad of 0 if w go i causal dirctio. Dcidig coditioal idpdc is hardr i o-causal dirctios. Causal odls ad coditioal idpdc s hardwird for huas!

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