Bayesian belief networks: Inference

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1 C 740 Knowd rprntton ctur 0 n f ntwork: nfrnc o ukrcht o@c.ptt.du 539 nnott qur C 750 chn rnn n f ntwork. 1. Drctd ccc rph Nod rndo vr nk n nk ncod ndpndnc. urr rthquk r ohnc rc C 750 chn rnn

2 n f ntwork. oc condton dtruton rt vr nd thr prnt urr rthquk ohnc r rc C 750 chn rnn u ont dtruton n N u ont dtruton dfnd n tr of oc condton dtruton otnd v th chn ru: X 1 X.. X n p: 1.. n X u th foown nnt of vu to rndo vr C 750 chn rnn p X hn t prot :

3 rtr copt pro n th N th fu ont dtruton dfnd : X 1 X.. X n X p X 1.. n Wht dd w v? r p: 5 nr ru vr # of prtr of th fu ont: urr 5 3 On prtr for fr: # of prtr of th N:? ohnc r rthquk rc C 750 chn rnn rtr copt pro n th N th fu ont dtruton dfnd : X 1 X.. X n X p X 1.. n Wht dd w v? r p: 5 nr ru vr # of prtr of th fu ont: urr 5 3 On prtr for fr: # of prtr of th N: C 750 chn rnn ohnc On prtr n vr condton for fr:? r rthquk rc

4 rtr copt pro n th N th fu ont dtruton dfnd : X 1 X.. X n X p X 1.. n Wht dd w v? r p: 5 nr ru vr # of prtr of th fu ont: urr 5 3 On prtr for fr: # of prtr of th N: ohnc On prtr n vr condton for fr: r rthquk rc C 750 chn rnn nfrnc n n ntwork N od copct th fu ont dtruton tkn dvnt of tn ndpndnc twn vr r nur of prtr ut w r ntrtd n ovn vrou nfrnc tk: Dnotc tk. fro ffct to cu urr ohnc rdcton tk. fro cu to ffct ohnc urr Othr protc qur qur on ont dtruton. r Quton: Cn w tk dvnt of ndpndnc to contruct pc orth nd pdup th nfrnc? C 750 chn rnn

5 nfrnc n n ntwork d nw: ct nfrnc pro n N N-hrd Coopr pprot nfrnc N-hrd Du u ut vr oftn w cn chv nfcnt provnt u our r ntwork urr rthquk r ohnc rc u w wnt to coput: C 750 chn rnn nfrnc n n ntwork Coputn: pproch 1. nd pproch. u out un-ntnttd vr fro th fu ont pr th ont dtruton product of condton Coputton cot: Nur of ddton:? Nur of product:? C 750 chn rnn

6 C 750 chn rnn nfrnc n n ntwork Coputn: pproch 1. nd pproch. u out un-ntnttd vr fro th fu ont pr th ont dtruton product of condton Coputton cot: Nur of ddton: 15 Nur of product:? C 750 chn rnn nfrnc n n ntwork Coputn: pproch 1. nd pproch. u out un-ntnttd vr fro th fu ont pr th ont dtruton product of condton Coputton cot: Nur of ddton: 15 Nur of product: 16*464

7 C 750 chn rnn nfrnc n n ntwork pproch. ntrv u nd product Con u nd product n rt w utpcton contnt cn tkn out of th u Coputton cot: Nur of ddton: 1+*[1+1+*1]? Nur of product: *[+*1+*1]? ] [. ]] [ ][ [ C 750 chn rnn nfrnc n n ntwork pproch. ntrv u nd product Con u nd product n rt w utpcton contnt cn tkn out of th u Coputton cot: Nur of ddton: 1+*[1+1+*1]9 Nur of product: *[+*1+*1]? ] [. ]] [ ][ [

8 C 750 chn rnn nfrnc n n ntwork pproch. ntrv u nd product Con u nd product n rt w utpcton contnt cn tkn out of th u Coputton cot: Nur of ddton: 1+*[1+1+*1]9 Nur of product: *[+*1+*1]16 ] [. ]] [ ][ [ C 750 chn rnn nfrnc n n ntwork h rt ntrvn of u nd product cn hp u to pd up th coputton of ont prot qur Wht f w wnt to coput: ot of hrd coputton rt chn of rut cn v th t for or qur ] [ ] [

9 nfrnc n n ntwork ct nfrnc orth: Vr nton Rcurv dcopoton Coopr Drwch f propton orth r rc rvr Otd chchtr pprot nfrnc orth: ont Cro thod: orwrd pn khood pn Vrton thod C 750 chn rnn Vr nton Vr nton: ntrv u nd product on vr t th t durn th nfrnc pc r on pc tructur cd ont tr tht roup tothr utp vr.. Qur rqur to nt nd th cn don n dffrnt ordr C 750 chn rnn

10 C 750 chn rnn Vr nton u th nton ordr: to ccut C 750 chn rnn ctor ctor: functon tht p vu nnt for ut of rndo vr to R r h cop of th fctor: t of vr dfnn th fctor p: u dcrt rndo vr wth vu 1 3 nd wth vu 1 nd ctor: cop of th fctor: } {

11 C 750 chn rnn ctor roduct * 3 * 3 * * * * 0.1* *0.1 1 * 1 * 1 0.5* * z z. C 750 chn rnn ctor roduct * 3 * 3 * * * * 0.1* *0.1 1 * 1 * 1 0.5* * z z.

12 C 750 chn rnn ctor u rnzton z z C 750 chn rnn ctor u rnzton z z

13 C 750 chn rnn Vr nton h ordr n whch vr r ntd ffct th ffcnc of th vr nton proc u th foown N nd ccuton of o: cohrnc ntnc dffcut rd ttr o hpp C 750 chn rnn Vr nton Ccuton prford n tr of fctor:... d h d c d c h d h d c d c p D C D D C C D

14 Vr nton rc 1: C D C 750 chn rnn Vr nton rc 1: C D Copt: 4 vr 1 ud w C 750 chn rnn

15 Vr nton rc : C D C 750 chn rnn Vr nton rc : C D Copt: 6 vr ud 1 ud out C 750 chn rnn

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