Bayesian belief networks
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- Darleen Parsons
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1 CS 2750 oundtions of I Lctur 9 ysin lif ntworks ilos Huskrcht ilos@cs.pitt.du 5329 Snnott Squr. Huskrcht odling uncrtinty with proilitis Dfining th full joint distriution ks it possil to rprsnt nd rson with uncrtinty in unifor wy W r l to hndl n ritrry infrnc prol rols: Spc coplxity. o stor full joint distriution w nd to rr Od n nurs. n nur of rndo vrils d nur of vlus Infrnc ti coplxity. o coput so quris rquirs Od. n stps. cquisition prol. Who is going to dfin ll of th proility ntris?. Huskrcht
2 ysin lif ntworks Ns ysin lif ntworks. Rprsnt th full joint distriution ovr th vrils or copctly with sllr nur of prtrs. k dvntg of conditionl nd rginl indpndncs ong rndo vrils nd r indpndnt nd r conditionlly indpndnt givn C C C C C C. Huskrcht lr syst xpl ssu your hous hs n lr syst ginst urglry. You liv in th sisiclly ctiv r nd th lr syst cn gt occsionlly st off y n rthquk. You hv two nighors ry nd ohn who do not know ch othr. If thy hr th lr thy cll you ut this is not gurntd. W wnt to rprsnt th proility distriution of vnts: urglry rthquk lr ry clls nd ohn clls Cusl rltions urglry rthquk lr ohnclls ryclls. Huskrcht 2
3 ysin lif ntwork. Dirctd cyclic grph Nods = rndo vrils urglry rthquk lr ry clls nd ohn clls Links = dirct cusl dpndncis twn vrils. h chnc of lr is influncd y rthquk h chnc of ohn clling is ffctd y th lr urglry rthquk lr ohnclls ryclls. Huskrcht ysin lif ntwork 2. Locl conditionl distriutions rlt vrils nd thir prnts urglry rthquk lr ohnclls ryclls. Huskrcht 3
4 ysin lif ntwork urglry ohnclls lr rthquk ryclls Huskrcht ysin lif ntworks gnrl wo coponnts: Dirctd cyclic grph Nods corrspond to rndo vrils issing links ncod indpndncs rtrs Locl conditionl proility distriutions for vry vril-prnt configurtion i p i Whr: p i S S - stnd for prnts of i Huskrcht 4
5 5. Huskrcht ull joint distriution in Ns ull joint distriution is dfind in trs of locl conditionl distriutions otind vi th chin rul: n i i i n p xpl: hn its proility is: ssu th following ssignnt of vlus to rndo vrils. Huskrcht ysin lif ntworks Ns ysin lif ntworks Rprsnt th full joint distriution ovr th vrils or copctly using th product of locl conditionls. ut how did w gt to locl prtriztions? nswr: Chin rul + Grphicl structur ncods conditionl nd rginl indpndncs ong rndo vrils nd r indpndnt nd r conditionlly indpndnt givn C h grph structur iplis th dcoposition!!! C C C C C
6 Indpndncs in Ns 3 sic indpndnc structurs: urglry urglry rthquk lr lr lr ohnclls ryclls ohnclls. Huskrcht Indpndncs in Ns urglry urglry rthquk lr lr lr ohnclls ryclls ohnclls. ohnclls is indpndnt of urglry givn lr. Huskrcht 6
7 Indpndncs in Ns urglry urglry rthquk lr lr lr ohnclls ryclls ohnclls 2. urglry is indpndnt of rthquk not knowing lr urglry nd rthquk co dpndnt givn lr!!. Huskrcht Indpndncs in Ns. 2. urglry urglry rthquk 3. lr lr lr ohnclls ryclls ohnclls 3. ryclls is indpndnt of ohnclls givn lr. Huskrcht 7
8 Indpndncs in N N distriution odls ny conditionl indpndnc rltions ong distnt vrils nd sts of vrils hs r dfind in trs of th grphicl critrion clld d- sprtion D-sprtion nd indpndnc Lt Y nd Z thr sts of nods If nd Y r d-sprtd y Z thn nd Y r conditionlly indpndnt givn Z D-sprtion : is d-sprtd fro givn C if vry undirctd pth twn th is lockd with C th locking 3 css tht xpnd on thr sic indpndnc structurs. Huskrcht Undirctd pth locking is d-sprtd fro givn C if vry undirctd pth twn th is lockd C. Huskrcht 8
9 Undirctd pth locking is d-sprtd fro givn C if vry undirctd pth twn th is lockd C. Huskrcht Undirctd pth locking is d-sprtd fro givn C if vry undirctd pth twn th is lockd C. th locking with linr sustructur in Z in C Z Y Y in. Huskrcht 9
10 Undirctd pth locking is d-sprtd fro givn C if vry undirctd pth twn th is lockd 2. th locking with th wdg sustructur Z in Z in C Y Y in. Huskrcht Undirctd pth locking is d-sprtd fro givn C if vry undirctd pth twn th is lockd 3. th locking with th v sustructur in Z Y in Y Z or ny of its dscndnts not in C. Huskrcht 0
11 Indpndncs in Ns urglry rthquk lr RdioRport ohnclls ryclls rthquk nd urglry r indpndnt givn ryclls?. Huskrcht Indpndncs in Ns urglry rthquk lr RdioRport ohnclls ryclls rthquk nd urglry r indpndnt givn ryclls urglry nd ryclls r indpndnt not knowing lr? CS 57 Intro to I. Huskrcht
12 Indpndncs in Ns urglry rthquk lr RdioRport ohnclls ryclls rthquk nd urglry r indpndnt givn ryclls urglry nd ryclls r indpndnt not knowing lr urglry nd RdioRport r indpndnt givn rthquk?. Huskrcht Indpndncs in Ns urglry rthquk lr RdioRport ohnclls ryclls rthquk nd urglry r indpndnt givn ryclls urglry nd ryclls r indpndnt not knowing lr urglry nd RdioRport r indpndnt givn rthquk urglry nd RdioRport r indpndnt givn ryclls?. Huskrcht 2
13 Indpndncs in Ns urglry rthquk lr RdioRport ohnclls ryclls rthquk nd urglry r indpndnt givn ryclls urglry nd ryclls r indpndnt not knowing lr urglry nd RdioRport r indpndnt givn rthquk urglry nd RdioRport r indpndnt givn ryclls. Huskrcht ysin lif ntworks Ns ysin lif ntworks Rprsnts th full joint distriution ovr th vrils or copctly using th product of locl conditionls. So how did w gt to locl prtriztions? 2.. n i i.. n p i h dcoposition is iplid y th st of indpndncs ncodd in th lif ntwork.. Huskrcht 3
14 4. Huskrcht ull joint distriution in Ns Rwrit th full joint proility using th product rul:. Huskrcht ull joint distriution in Ns Rwrit th full joint proility using th product rul: roduct rul
15 5. Huskrcht ull joint distriution in Ns Rwrit th full joint proility using th product rul: roduct rul. Huskrcht ull joint distriution in Ns Rwrit th full joint proility using th product rul: roduct rul
16 6. Huskrcht ull joint distriution in Ns Rwrit th full joint proility using th product rul:. Huskrcht ull joint distriution in Ns Rwrit th full joint proility using th product rul:
17 7. Huskrcht ull joint distriution in Ns Rwrit th full joint proility using th product rul:. Huskrcht ull joint distriution in Ns Rwrit th full joint proility using th product rul:
18 rtr coplxity prol In th N th full joint distriution is dfind s: 2.. n i p i i.. n Wht did w sv? lr xpl: inry ru ls vrils # of prtrs of th full joint:? urglry rthquk lr ohnclls ryclls. Huskrcht rtr coplxity prol In th N th full joint distriution is dfind s: 2.. n i p i i.. n Wht did w sv? lr xpl: inry ru ls vrils # of prtrs of th full joint: On prtr is for fr: # of prtrs of th N:? urglry ohnclls lr rthquk ryclls. Huskrcht 8
19 ysin lif ntwork: prtrs count otl: 20 urglry ohnclls lr rthquk ryclls Huskrcht rtr coplxity prol In th N th full joint distriution is dfind s: 2.. n i p i i.. n Wht did w sv? lr xpl: 5 inry ru ls vrils # of prtrs of th full joint: urglry On prtr is for fr: # of prtrs of th N: ohnclls On prtr in vry conditionl is for fr:? lr rthquk ryclls. Huskrcht 9
20 ysin lif ntwork: fr prtrs urglry otl fr prs: 0 ohnclls lr rthquk ryclls = = Huskrcht rtr coplxity prol In th N th full joint distriution is dfind s: 2.. n i p i i.. n Wht did w sv? lr xpl: 5 inry ru ls vrils # of prtrs of th full joint: urglry On prtr is for fr: # of prtrs of th N: ohnclls On prtr in vry conditionl is for fr: lr rthquk ryclls. Huskrcht 20
21 odl cquisition prol h structur of th N typiclly rflcts cusl rltions Ns r lso soti rfrrd to s cusl ntworks Cusl structur is intuitiv in ny pplictions doin nd it is rltivly sy to dfin to th doin xprt roility prtrs of N r conditionl distriutions rlting rndo vrils nd thir prnts Coplxity is uch sllr thn th full joint It is uch sir to otin such proilitis fro th xprt or lrn th utoticlly fro dt. Huskrcht Ns uilt in prctic In vrious rs: Intllignt usr intrfcs icrosoft roulshooting dignosis of tchnicl dvic dicl dignosis: thfindr Intllipth CSC unin QR-D Collortiv filtring ilitry pplictions usinss nd finnc Insurnc crdit pplictions. Huskrcht 2
22 Dignosis of cr ngin Dignos th ngin strt prol. Huskrcht Cr insurnc xpl rdict cli costs dicl liility sd on ppliction dt. Huskrcht 22
23 ICU lr ntwork. Huskrcht CCS Coputr-sd tint Cs Siultion syst CCS- dvlopd y rkr nd illr Univrsity of ittsurgh 422 nods nd 867 rcs. Huskrcht 23
24 QR-D dicl dignosis in intrnl dicin U sd ittsurgh on QR syst uilt t U ittsurgh iprtit ntwork of diss/findings rltions. Huskrcht Infrnc in ysin ntworks N odls copctly th full joint distriution y tking dvntg of xisting indpndncs twn vrils Siplifis th cquisition of proilistic odl ut w r intrstd in solving vrious infrnc tsks: Dignostic tsk. fro ffct to cus urglry ohnclls rdiction tsk. fro cus to ffct ohnclls urglry Othr proilistic quris quris on joint distriutions. lr in issu: Cn w tk dvntg of indpndncs to construct spcil lgoriths nd spding up th infrnc?. Huskrcht 24
25 Infrnc in ysin ntwork d nws: xct infrnc prol in Ns is N-hrd Coopr pproxit infrnc is N-hrd Dgu Luy ut vry oftn w cn chiv significnt iprovnts ssu our lr ntwork urglry rthquk lr ohnclls ryclls ssu w wnt to coput:. Huskrcht Infrnc in ysin ntworks Coputing: pproch. lind pproch. Su out ll un-instntitd vrils fro th full joint xprss th joint distriution s product of conditionls Coputtionl cost: Nur of dditions:? Nur of products:?. Huskrcht 25
26 26. Huskrcht Infrnc in ysin ntworks Coputing: pproch. lind pproch. Su out ll un-instntitd vrils fro th full joint xprss th joint distriution s product of conditionls Coputtionl cost: Nur of dditions: 5 Nur of products:?. Huskrcht Infrnc in ysin ntworks Coputing: pproch. lind pproch. Su out ll un-instntitd vrils fro th full joint xprss th joint distriution s product of conditionls Coputtionl cost: Nur of dditions: 5 Nur of products: 6*4=64
27 27. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of dditions:? Nur of products:?.. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of dditions:?
28 28. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of dditions:? 2*. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of dditions:? 2*2*
29 29. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of dditions:? 2*2* 2*. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of dditions:? 2*2* 2* 2*
30 30. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of dditions: +2*[++2*]=9 2*2* 2* 2*. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of products:?
31 3. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of products:? 2*2 *2*. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of products:? 2*2 *2* 2*2* 2*2
32 32. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of products: 2*[2+2*+2*]=6 2*2 *2* 2*2* 2*2. Huskrcht Infrnc in ysin ntworks pproch 2. Intrlv sus nd products Coins sus nd product in srt wy ultiplictions y constnts cn tkn out of th su Coputtionl cost: Nur of dditions: +2*[++2*]=9 Nur of products: 2*[2+2*+2*]=6.
33 33. Huskrcht Vril liintion Vril liintion: Siilr id ut intrlv su nd products on vril t th ti during infrnc.g. Qury rquirs to liint nd this cn don in diffrnt ordr. Huskrcht Vril liintion ssu ordr: to clcult
34 34. Huskrcht Vril liintion ssu ordr: to clcult. Huskrcht Vril liintion ssu ordr: to clcult
35 35. Huskrcht Vril liintion ssu ordr: to clcult. Huskrcht Vril liintion ssu ordr: to clcult
36 36. Huskrcht Vril liintion ssu ordr: to clcult. Huskrcht Vril liintion ssu ordr: to clcult
37 37. Huskrcht Vril liintion ssu ordr: to clcult 2. Huskrcht Vril liintion ssu ordr: to clcult 2
38 38. Huskrcht Vril liintion ssu ordr: to clcult 2. Huskrcht Infrnc in ysin ntwork xct infrnc lgoriths: Vril liintion Rcursiv dcoposition Coopr Drwich Syolic infrnc D rosio lif propgtion lgorith rl Clustring nd joint tr pproch Luritzn Spiglhltr rc rvrsl Olstd Schchtr pproxit infrnc lgoriths: ont Crlo thods: orwrd spling Liklihood spling Vritionl thods ook ook ook
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