21第五章不确定性推理方法(简s1)

•••Bayes•••Bayes-¾¾¾T(E1E2)=Min{T(E1),T(E2)}T(E1E2)=Max{T(E1),T(E2)}T(E1E2)=T(E1)T(E2)T(E1E2)=T(E1)T(E2)T(E1)T(E2))0)(()()()/(=APAPABPABP)0)(()/()()(=APABPAPABP)0)(()/()()(=BPBAPBPABPSAnBBB...,,21),,2,1(0)(niBPiL=)/()(...)/()()/()()(2211nnBAPBPBAPBPBAPBPAP+++=BayesSA:nBBB...,,21),,2,1(0)(,0)(niBPAPiL=)/()(...)/()()/()()()()/(11nniiiiBAPBPBAPBPBAPBPAPABPABP++==Bayes12A“”3A“”4A“”•AAnBBB...,,21)(mBPmBmB)/(ABPm)(mBP:)()()|()()|(iiiiBPAPBAPBPABP×=nBBB...,,21)(mBPmB)/(ABPm:)()()|()()|(iiiiBPAPBAPBPABP×=Bayes•1976Prospector•–•/•/–•••Bayes¬Bayes¾P(A|A’):A’A[0,1]¾P(A|A’)¾C(A|A’)[-a,a]P(A|A’)A1’A2’A3’A100g/LP(B)P(B|A),AP(B|A),AP(B|A’)AP(A),P(A|A’)LS,LN)(1)()(xPxPxQ−=•Q(x)P(x)•P(x)[0,1]Q(x)[0,+]P(X)0Q(X)0,XP(X)0.5Q(X)1P(X)1Q(X)X⎯⎯⎯→⎯⎪⎪⎩⎪⎪⎨⎧¬¬=¬=⇒)()()|()|()()()|()|(APBPBAPABPAPBPBAPABPBayes⎯→⎯⎪⎩⎪⎨⎧¬=×=)|()|()()|(BAPBAPLSBQLSABQ1)()1()()|(+×−×=BPLSBPLSABP(2)LS:Q(B|A)=LSQ(B)LS1Q(B|A)Q(B)P(B|A)P(B)A∃B,LSP(B|A),LS⇒Q(B|A),P(B|A)1,LSLS=1Q(B|A)=Q(B)P(B|A)=P(B)A∃BLS(0,1)Q(B|A)Q(B)P(B|A)P(B)A∃B,LSP(B|A)LS=0Q(B|A)=0P(B|A)=0A∃B¾LS=P(A|B)/P(A|B)LS¾LS2AP(A)=P(A|A’)=0P(A)=1(1)P(B|A)⎯⎯⎯→⎯⎪⎪⎩⎪⎪⎨⎧¬¬¬¬=¬¬¬¬=¬⇒)()()|()|()()()|()|(APBPBAPABPAPBPBAPABPBayes⎯→⎯⎪⎩⎪⎨⎧¬¬¬=×=¬)|()|()()|(BAPBAPLNBQLNABQ1)()1()()|(+×−×=¬BPLNBPLNABP(2)LN:Q(B|A)=LNQ(B)LN1Q(B|A)Q(B)P(B|A)P(B)A∃B,LNP(B|A),LN⇒Q(B|A),P(B|A)1LN=1Q(B|A)=Q(B)P(B|A)=P(B)A∃BLN(0,1)Q(B|A)Q(B)P(B|A)P(B)A∃B,LNP(B|A)A∃BLNLN=0Q(B|A)=0P(B|A)=0LN0⇒B⇔B⇒A∃¾LN=P(A|B)/P(A|B)LN¾LN¾?)|(),|()3,2,1(3,2,13.005.003.0)002.0,1()1,20()1,10(=¬==⎪⎩⎪⎨⎧⎪⎩⎪⎨⎧iiiiiiiABPABPiAiBTHENAIF⎪⎩⎪⎨⎧=↑=↑==+×−×=3,3.02,51.01,24.01)()1()()|()3,2,1(1iiiBPLSBPLSABPiAiiiiiii⎪⎩⎪⎨⎧↓====+×−׬=3503,00086.02,05.01,03.01)()1()()|()3,2,1(2iiiBPLNBPLNABPiAiiiiiii30P(A|A’)1(1)Dudd()P(B|A’)=P(B|A)P(A|A’)+P(B|A)P(A|A’)*P(B|A),A*AA*P(A|A’)=t,P(B|A’)=tP(B|A)+(1-t)P(B|A)2P(B|A')P(A|A')P(B|A')1P(B|A)[0,P(A)])'|()()|()()|(AAPAPABPBPABP׬−+¬0P(B|A)P(A)P(B)[P(A),1])]()'|([)(1)()|()(APAAPAPBPABPBP−×−−+P(B|A')=P(B|A)P(A|A')+P(B|A)P(A|A')O1P(B|A')P(B|A)P(B)P(B|-A)P(A)P(A|A')(3)P(A)⎪⎪⎩⎪⎪⎨⎧∈−×−−+∈׬−+¬=]1),([)'/()]()'/([)(1)()/()()](,0[)'/()'/()()/()()/()'/(APAAPAPAAPAPBPABPBPAPAAPAAPAPABPBPABPABP⎪⎪⎩⎪⎪⎨⎧¬=−===≤≤≤≤iininininiAAAAPAAAAAAPAAAAAAPAAP),'|(1)},'|({max)},'|({min)'|(211211ULUUL(5)NBAi’↔AiB)()()'|()()'|()()'|()',,','|(2121BQBQABQBQABQBQABQAAABQnn××××=44444443444444421LL•P(A)=1,P(B1)=0.04,P(B2)=0.02P(B2|A)R1:AB1LS=20LN=1R2:B1B2LS=300LN=0.001•⎪⎩⎪⎨⎧∈⇐⇐⇐⎯→⎯)(),|(]1),(?[)],(,0?[)'|(',,)|(11122BPABPAPAPAAPAABABBABP⎪⎩⎪⎨⎧==+×−×=+×−×=⇔⎩⎨⎧04.0)(454.0104.0)120(04.0201)()1()()|(*)()|(11111111BPBPLSBPLSABPBPABPAB1B2⎪⎪⎩⎪⎪⎨⎧≤≤−×−−+≤׬−+¬=1)'/()()]()'/([)(1)()/()()()'/(0)'/()()/()()/()'/(AAPAPAPAAPAPBPABPBPAPAAPAAPAPABPBPABPABPA’AB)]()|([)(1)()|()()|(11121222BPABPBPBPBBPBPABP−×−−+=)(859.0102.0)1300(02.03001)()1()()|(1222212BBPLSBPLSBBP=+×−×=+×−×=382.0]04.0454.0[04.0102.0859.0.020)|(2=−×−−+=ABP••2211''AAAA⎯→←⎯→←B1⎪⎪⎩⎪⎪⎨==+×−×+×−=+×−×=2,903.0103.0)1300(03.0300103.0)120(1)()1()()|(111iBPLSBPLSABPiii⎧==×1,382.003.020i99464.01903.0)120(903.0201382.0)1300(382.03001)|()1()|(1)|()1()|()|(211211112112211=+×−×=+×−×=+×−×=+×−×=ABPLSABPLSABPLSABPLSAABP99464.0)|(1)|()|(03.003.01903.01903.0382.01382.0)()(1)|(1)|()|(1)|()()()|()()|()|(211211211221121211=+=−×−×−=−×′−′×′−′=×′×′=AABQAABQAABPBPBPABPABPABPABPBQBQABQBQABQAABQ•Bayes–•–•Bj•P(B|A’)P(Bi)••’•–––––•––•–––•⎪⎪⎩⎪⎪⎨⎧≥≥−=P(B)A),P(B|P(B))P(B|A)-P(BP(B)|A),P(BP(B))P(B|A)-P(BCF(B,A)001-1CF(B,A)1¾,3,8.02,8.01,7.0)|(,3,78.02,7.01,1.0)(⎪⎩⎪⎨⎧====⎪⎩⎪⎨⎧====iiiABPiiiBPiii,3,11/12,3/11,3/2),(⎪⎩⎪⎨⎧====iiiABCFii•CF(B,A)–CF(B,A)=1–CF(B,A)=-1–CF(B,A)=0•CF(B,A)P(B|A),P(B)•CF(A)-1CF(A)•CF(A)=1CF(A)=-1CF(A)=0•CF(A)ACF(A)CF(A)ACF(A)•“”•“”•“”•·“”•CF(B)CF(B)CF(B)⎪⎪⎪⎩⎪⎪⎪⎨⎧−+++≥≥+=(B)CF(B)CF|})(||,)(min{|1(B)CF(B)CF0(B)CF0(B)CF(B)CF(B)CF(B)CF(B)CF0(B)CF0(B)CF(B)CF(B)CF-(B)CF(B)CFCF(B)212121212121212121BCFBCF•CF(A)ABCF(B,A)CF(B)CF(B|A)•CF(B)–ACF(A)=1⎪⎪⎪⎩⎪⎪⎪⎨⎧−+++≥≥+=A)CF(B,CF(B)|}A)CF(B,||,CF(B)min{|1A)CF(B,CF(B)0A)CF(B,0CF(B)CF(B))A)(1CF(B,CF(B)0A)CF(B,0CF(B)CF(B))-A)(1CF(B,CF(B)A)|CF(B–ACF(A)1•0CF(A)1CF(A)CF(B,A)CF(A)=1CF(B,A)•CF(A)0A→BMYCINCF(A)≤0.2⎪⎪⎪⎩⎪⎪⎪⎨⎧⋅−⋅+⋅+⋅+≥⋅≥⋅+=)},()(||,)(min{|1A)CF(B,)(CF(B)0A)CF(B,)(0CF(B)CF(B))A)(1CF(B,)(CF(B)0A)CF(B,)(0CF(B)CF(B))-A)(1CF(B,)(CF(B)A)|CF(BABCFACFBCFACFACFACFACFACF•R1A1B1CFB1A10.8R2A2B1CFB1A20.5R3B1A3B2CFB2B1A30.8CFA1CFA2CFA31CFB1=CFB2=0•CFB1CFB2••R1CFB1|A1CF(B1)CF(B1,A1)(1CF(B1))0+0.81=0.8CFB10.8•R2CFB1|A2CF(B1)CF(B1A2)(1CF(B1))0.8+0.50.2=0.9CFB10.9•R310.9CFB1A3minCFA3CFB10.9CFB1A31CF(B2|B1A3)=CF(B2)+CF(B1A3)CF(B2,B1A3)(1-CF(B2))=0+0.90.8(1-0)=0.72•CFB10.9CFB20.72•––♦♦♦••Basicprobabilityassignment:BPAUineeeeU},,,,{21L=nA2~=U},|{~~UAAAA⊆=⎪⎩⎪⎨⎧≥==→∑⊆AAMAMMMMUAnn0)(1)(20)(],1,0[2:φAM~*U={}},,,{~821AAAAL=¾U238¾AiM(Ai)[0,1],Ai=1¾A1={},A2={},A3={},A4={},A5={},A6={},A7={},A8={∅}M(A1)=0.3,M(A2)=M(A8)=0,M(A3)=M(A6)=M(A7)=0.1M(A4)=M(A5)=0.2¾M(Ai)Ai™™™™™™™BPA•Example:diseasediagnosticsU={Allergy,Flu,Cold,Pneumonia}•BPA:m:2|U|→[0,1]m1:{Flu,Cold,Pneu}0.6U:0.4Example•Patienthascholestaticjaundice•Possiblecausesare:–Hepatitis(hep)–Cirrhosis(cirr)–Gallstone(gall)–Pancreaticcancer(pan)Thismu