Bayesian belief networks

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1 CS 1571 Introducton to I Lctur 20 ysn lf ntworks los Huskrcht los@cs.ptt.du 5329 Snnott Squr CS 1571 Intro to I. Huskrcht odlng uncrtnty wth prolts Dfnng th full jont dstruton ks t possl to rprsnt nd rson wth uncrtnty n unfor wy W r l to hndl n rtrry nfrnc prol rols: Spc coplxty. o stor full jont dstruton w nd to rr Od n nurs. n nur of rndo vrls d nur of vlus Infrnc t coplxty. o coput so qurs rqurs Od. n stps. cquston prol. Who s gong to dfn ll of th prolty ntrs? CS 1571 Intro to I. Huskrcht 1

2 ysn lf ntworks Ns ysn lf ntworks. Rprsnt th full jont dstruton ovr th vrls or copctly wth sllr nur of prtrs. k dvntg of condtonl nd rgnl ndpndncs ong rndo vrls nd r ndpndnt nd r condtonlly ndpndnt gvn C C C C C C CS 1571 Intro to I. Huskrcht lr syst xpl ssu your hous hs n lr syst gnst urglry. You lv n th ssclly ctv r nd th lr syst cn gt occsonlly st off y n rthquk. You hv two nghors ry nd ohn who do not know ch othr. If thy hr th lr thy cll you ut ths s not gurntd. W wnt to rprsnt th prolty dstruton of vnts: urglry rthquk lr ry clls nd ohn clls Cusl rltons urglry rthquk lr ohnclls ryclls CS 1571 Intro to I. Huskrcht 2

3 ysn lf ntwork 1. Drctd cyclc grph Nods = rndo vrls urglry rthquk lr ry clls nd ohn clls Lnks = drct cusl dpndncs twn vrls. h chnc of lr s nfluncd y rthquk h chnc of ohn cllng s ffctd y th lr urglry rthquk lr ohnclls ryclls CS 1571 Intro to I. Huskrcht ysn lf ntwork 2. Locl condtonl dstrutons rlt vrls nd thr prnts urglry rthquk lr ohnclls ryclls CS 1571 Intro to I. Huskrcht 3

4 ysn lf ntwork urglry ohnclls lr rthquk ryclls CS 1571 Intro to I. Huskrcht ysn lf ntworks gnrl wo coponnts: S S Drctd cyclc grph Nods corrspond to rndo vrls ssng lnks ncod ndpndncs rtrs Locl condtonl prolty dstrutons for vry vrl-prnt confgurton p Whr: p - stnd for prnts of CS 1571 Intro to I. Huskrcht 4

5 ull jont dstruton n Ns ull jont dstruton s dfnd n trs of locl condtonl dstrutons otnd v th chn rul: n xpl: 1.. n hn ts prolty s: ssu th followng ssgnnt of vlus to rndo vrls p CS 1571 Intro to I. Huskrcht ysn lf ntworks Ns ysn lf ntworks Rprsnt th full jont dstruton ovr th vrls or copctly usng th product of locl condtonls. ut how dd w gt to locl prtrztons? nswr: Chn rul + Grphcl structur ncods condtonl nd rgnl ndpndncs ong rndo vrls nd r ndpndnt nd r condtonlly ndpndnt gvn C C C C C C h grph structur pls th dcoposton!!! CS 1571 Intro to I. Huskrcht 5

6 Indpndncs n Ns 3 sc ndpndnc structurs: urglry urglry rthquk lr lr lr ohnclls ryclls ohnclls CS 1571 Intro to I. Huskrcht Indpndncs n Ns urglry urglry rthquk lr lr lr ohnclls ryclls ohnclls 1. ohnclls s ndpndnt of urglry gvn lr CS 1571 Intro to I. Huskrcht 6

7 Indpndncs n Ns urglry urglry rthquk lr lr lr ohnclls ryclls ohnclls 2. urglry s ndpndnt of rthquk not knowng lr urglry nd rthquk co dpndnt gvn lr!! CS 1571 Intro to I. Huskrcht Indpndncs n Ns urglry urglry rthquk 3. lr lr lr ohnclls ryclls ohnclls 3. ryclls s ndpndnt of ohnclls gvn lr CS 1571 Intro to I. Huskrcht 7

8 Indpndncs n N N dstruton odls ny condtonl ndpndnc rltons ong dstnt vrls nd sts of vrls hs r dfnd n trs of th grphcl crtron clld d- sprton D-sprton nd ndpndnc Lt Y nd Z thr sts of nods If nd Y r d-sprtd y Z thn nd Y r condtonlly ndpndnt gvn Z D-sprton : s d-sprtd fro gvn C f vry undrctd pth twn th s lockd wth C th lockng 3 css tht xpnd on thr sc ndpndnc structurs CS 1571 Intro to I. Huskrcht Undrctd pth lockng s d-sprtd fro gvn C f vry undrctd pth twn th s lockd C CS 1571 Intro to I. Huskrcht 8

9 Undrctd pth lockng s d-sprtd fro gvn C f vry undrctd pth twn th s lockd C CS 1571 Intro to I. Huskrcht Undrctd pth lockng s d-sprtd fro gvn C f vry undrctd pth twn th s lockd C 1. th lockng wth lnr sustructur n Z n C Z Y Y n CS 1571 Intro to I. Huskrcht 9

10 Undrctd pth lockng s d-sprtd fro gvn C f vry undrctd pth twn th s lockd 2. th lockng wth th wdg sustructur Z n Z n C Y Y n CS 1571 Intro to I. Huskrcht Undrctd pth lockng s d-sprtd fro gvn C f vry undrctd pth twn th s lockd 3. th lockng wth th v sustructur n Z Y n Y Z or ny of ts dscndnts not n C CS 1571 Intro to I. Huskrcht 10

11 Indpndncs n Ns urglry rthquk lr RdoRport ohnclls ryclls rthquk nd urglry r ndpndnt gvn ryclls urglry nd ryclls r ndpndnt not knowng lr urglry nd RdoRport r ndpndnt gvn rthquk urglry nd RdoRport r ndpndnt gvn ryclls CS 1571 Intro to I. Huskrcht ysn lf ntworks Ns ysn lf ntworks Rprsnts th full jont dstruton ovr th vrls or copctly usng th product of locl condtonls. So how dd w gt to locl prtrztons? n 1.. n p h dcoposton s pld y th st of ndpndncs ncodd n th lf ntwork. CS 1571 Intro to I. Huskrcht 11

12 12. Huskrcht CS 1571 Intro to I ull jont dstruton n Ns Rwrt th full jont prolty usng th product rul:. Huskrcht CS 1571 Intro to I # of prtrs of th full jont: rtr coplxty prol In th N th full jont dstruton s dfnd s: Wht dd w sv? lr xpl: 5 nry ru ls vrls urglry ohnclls lr rthquk ryclls n n p On prtr s for fr:

13 rtr coplxty prol In th N th full jont dstruton s dfnd s: n p 1.. n Wht dd w sv? lr xpl: 5 nry ru ls vrls # of prtrs of th full jont: urglry On prtr s for fr: # of prtrs of th N:? ohnclls lr rthquk ryclls CS 1571 Intro to I. Huskrcht ysn lf ntwork. In th N th full jont dstruton s xprssd usng st of locl condtonl dstrutons urglry ohnclls rthquk lr ryclls CS 1571 Intro to I. Huskrcht 13

14 urglry ohnclls ysn lf ntwork. In th N th full jont dstruton s xprssd usng st of locl condtonl dstrutons 2 2 rthquk lr ryclls CS 1571 Intro to I. Huskrcht rtr coplxty prol In th N th full jont dstruton s dfnd s: n p 1.. n Wht dd w sv? lr xpl: 5 nry ru ls vrls # of prtrs of th full jont: urglry On prtr s for fr: # of prtrs of th N: CS 1571 Intro to I ohnclls On prtr n vry condtonl s for fr: lr rthquk ryclls. Huskrcht 14

15 odl cquston prol h structur of th N typclly rflcts cusl rltons Ns r lso sot rfrrd to s cusl ntworks Cusl structur s ntutv n ny pplctons don nd t s rltvly sy to dfn to th don xprt rolty prtrs of N r condtonl dstrutons rltng rndo vrls nd thr prnts Coplxty s uch sllr thn th full jont It s uch sr to otn such prolts fro th xprt or lrn th utotclly fro dt CS 1571 Intro to I. Huskrcht Ns ult n prctc In vrous rs: Intllgnt usr ntrfcs crosoft roulshootng dgnoss of tchncl dvc dcl dgnoss: thfndr Intllpth CSC unn QR-D Collortv fltrng ltry pplctons usnss nd fnnc Insurnc crdt pplctons CS 1571 Intro to I. Huskrcht 15

16 Dgnoss of cr ngn Dgnos th ngn strt prol CS 1571 Intro to I. Huskrcht Cr nsurnc xpl rdct cl costs dcl llty sd on pplcton dt CS 1571 Intro to I. Huskrcht 16

17 ICU lr ntwork CS 1571 Intro to I. Huskrcht CCS Coputr-sd tnt Cs Sulton syst CCS- dvlopd y rkr nd llr Unvrsty of ttsurgh 422 nods nd 867 rcs CS 1571 Intro to I. Huskrcht 17

18 QR-D dcl dgnoss n ntrnl dcn U sd ttsurgh on QR syst ult t U ttsurgh prtt ntwork of dss/fndngs rltons CS 1571 Intro to I. Huskrcht Infrnc n ysn ntwork d nws: xct nfrnc prol n Ns s N-hrd Coopr pproxt nfrnc s N-hrd Dgu Luy ut vry oftn w cn chv sgnfcnt provnts ssu our lr ntwork urglry rthquk lr ohnclls ryclls ssu w wnt to coput: CS 1571 Intro to I. Huskrcht 18

19 19. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks Coputng: pproch 1. lnd pproch. Su out ll un-nstnttd vrls fro th full jont xprss th jont dstruton s product of condtonls Coputtonl cost: Nur of ddtons: 15 Nur of products: 16*4=64. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost:?. } { } { x x x f x f

20 20. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of ddtons:? 1. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of ddtons:? 2*1

21 21. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of ddtons:? 2*2*1. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of ddtons:? 2*2*1 2*1

22 22. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of ddtons:? 2*2*1 2*1 2*1 1. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of ddtons: 1+2*[1+1+2*1]=9 2*2*1 2*1 2*1 1

23 23. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of products:? 1. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of products:? 2*2 *2*1

24 24. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of products: 2*[2+2*1+2*1]=16 2*2 *2*1 2*2*1 2*2. Huskrcht CS 1571 Intro to I Infrnc n ysn ntworks pproch 2. Intrlv sus nd products Cons sus nd product n srt wy ultplctons y constnts cn tkn out of th su Coputtonl cost: Nur of ddtons: 1+2*[1+1+2*1]=9 Nur of products: 2*[2+2*1+2*1]=16.

25 25. Huskrcht CS 1571 Intro to I Vrl lnton Vrl lnton: Slr d ut ntrlv su nd products on vrl t th t durng nfrnc.g. Qury rqurs to lnt nd ths cn don n dffrnt ordr. Huskrcht CS 1571 Intro to I Vrl lnton ssu ordr: to clcult

26 Infrnc n ysn ntwork xct nfrnc lgorths: Vrl lnton ook Rcursv dcoposton Coopr Drwch Syolc nfrnc D roso lf propgton lgorth rl Clustrng nd jont tr pproch Lurtzn ook Spglhltr rc rvrsl Olstd Schchtr pproxt nfrnc lgorths: ont Crlo thods: ook orwrd splng Lklhood splng Vrtonl thods CS 1571 Intro to I. Huskrcht 26

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