Consider the following:
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onsider the following: d,h)/P(h) [P(d,l,b,h) + P(d,l,~b,h) + P(d,~l,b,h) + P(d,~l, P(d|l)P(l|h,b)P(b) + P(d|l)P(l|h,~b)P(~b) + P(d|~l)P(~l|h,b)P(b) + P(d|~l)P(~l|h,~b)P( H B E L F D P(b) P(h) P(e|h) P(e|~h) P(l|h,b) P(l|~h,b) P(l|h,~b) P(l|~h,~b) P(d|l) P(d|~l) P(f|e) P(f|~e) P(d|l)P(l|h,b) + P(d|~l)P(~l|h,b)] b)[P(d|l)P(l|h,~b) + P(d|~l)P(~l|h,~b)] P(d|l)[P(l|h,b)P(b) + P(l|h,~b)P(~b)] + P(d|~l)[P(~l|h,b)P(b) + P(~l|h,~b)P( = =
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Consider the following:. P(b). P(h). H B E L F D. P(e|h) P(e|~h). P(l|h,b) P(l|~h,b) P(l|h,~b) P(l|~h,~b). P(f|e) P(f|~e). P(d|l) P(d|~l). P( d|h ) = P( d,h )/P(h) - PowerPoint PPT Presentation
Transcript of Consider the following:
Consider the following:
P(d|h) = P(d,h)/P(h) = [P(d,l,b,h) + P(d,l,~b,h) + P(d,~l,b,h) + P(d,~l,~b,h)] / P(h) = P(d|l)P(l|h,b)P(b) + P(d|l)P(l|h,~b)P(~b) + P(d|~l)P(~l|h,b)P(b) + P(d|~l)P(~l|h,~b)P(~b)
H B
E L
F D
P(b)P(h)
P(e|h)P(e|~h)
P(l|h,b) P(l|~h,b)P(l|h,~b) P(l|~h,~b)
P(d|l)P(d|~l)
P(f|e)P(f|~e)
P(b)[P(d|l)P(l|h,b) + P(d|~l)P(~l|h,b)] + P(~b)[P(d|l)P(l|h,~b) + P(d|~l)P(~l|h,~b)]
P(d|l)[P(l|h,b)P(b) + P(l|h,~b)P(~b)]+ P(d|~l)[P(~l|h,b)P(b) + P(~l|h,~b)P(~b)]
= =
Consider the following:
P(d|h) = P(d,h)/P(h) = [P(d,l,b,h) + P(d,l,~b,h) + P(d,~l,b,h) + P(d,~l,~b,h)] / P(h) = P(d|l)P(l|h,b)P(b) + P(d|l)P(l|h,~b)P(~b) + P(d|~l)P(~l|h,b)P(b) + P(d|~l)P(~l|h,~b)P(~b)
H B
E L
F D
P(b) , P(~b)f(H)
f(E,H)P(l|h,b) P(l|~h,b) P(~l|h,b) P(~l|~h,b)
P(l|h,~b) P(l|~h,~b) P(~l|h,~b) P(~l|~h,~b)
f(d,L) = [P(d|l), P(d|~l)]f(F,E)
P(b)[P(d|l)P(l|h,b) + P(d|~l)P(~l|h,b)] + P(~b)[P(d|l)P(l|h,~b) + P(d|~l)P(~l|h,~b)]
= ΣB P(B) ΣL P(d|L)P(L|h,B)= ΣB f(B) ΣL f(d,L)f(L,h,B)
P(d|l)[P(l|h,b)P(b) + P(l|h,~b)P(~b)]+ P(d|~l)[P(~l|h,b)P(b) + P(~l|h,~b)P(~b)]
= ΣL P(d|L) ΣB P(L|h,B)P(B)
= =
f(B)
f(L,h,B)
Consider the following:
P(b)[P(d|l)P(l|h,b) + P(d|~l)P(~l|h,b)] + P(~b)[P(d|l)P(l|h,~b) + P(d|~l)P(~l|h,~b)] = ΣB f(B) ΣL f(d,L)f(L,h,B)
P(l|h,b)
P(l|h,~b)
P(~l|h,b)
P(~l|h,~b)
P(d|l)
P(d|~l)
P(d|l)P(l|h,b)
P(d|l)P(l|h,~b)
P(d|~l)P(~l|h,b)
P(d|~l)P(~l|h,~b)
[ P(d|l)P(l|h,b) + P(d|~l)P(~l|h,b)]
[ P(d|l)P(l|h,~b) + P(d|~l)P(~l|h,~b) ]
f(d,L,h,B) =f(d,L)f(L,h,B)
f(d,h,B)ΣL f(d,L)f(L,h,B)
Sum over different L values for same B values
f(B)f(d,h,B)f(B)
P(b)
P(~b)
P(b)[P(d|l)P(l|h,b) + P(d|~l)P(~l|h,b)]
P(~b)[P(d|l)P(l|h,~b) + P(d|~l)P(~l|h,~b)]
then sum over different BValues
f(d,L)
H B
E L
F D
P(b) , P(~b)f(H)
f(E,H)P(l|h,b) P(l|~h,b) P(~l|h,b) P(~l|~h,b)
P(l|h,~b) P(l|~h,~b) P(~l|h,~b) P(~l|~h,~b)
f(d,L) = [P(d|l), P(d|~l)]f(F,E)
f(B)
f(L,h,B)
f(L,h,B)
Consider the following:
… = P(d|l)P(l|h,b)P(b) + P(d|l)P(l|h,~b)P(~b) + P(d|~l)P(~l|h,b)P(b) + P(d|~l)P(~l|h,~b)P(~b)
P(b)[P(d|l)P(l|h,b) + P(d|~l)P(~l|h,b)] + P(~b)[P(d|l)P(l|h,~b) + P(d|~l)P(~l|h,~b)]
= ΣB f(B) ΣL f(d,L)f(L,h,B)
P(d|l)[P(l|h,b)P(b) + P(l|h,~b)P(~b)]+ P(d|~l)[P(~l|h,b)P(b) + P(~l|h,~b)P(~b)]
= ΣL f(d|L) ΣB f(L,h,B)f(B)
= =
1. Eliminate B (factor FB2 (L))
2. Eliminate L (factor FL2 ())
1. Eliminate L (factor FL1 (B))
2. Eliminate B (factor FB1 ())
H B
E L
F D
P(b) , P(~b)f(H)
f(E,H)P(l|h,b) P(l|~h,b) P(~l|h,b) P(~l|~h,b)
P(l|h,~b) P(l|~h,~b) P(~l|h,~b) P(~l|~h,~b)
f(d,L) = [P(d|l), P(d|~l)]f(F,E)
f(B)
f(L,h,B)
Consider the following:
P(d) = [P(d,l,b,h) + P(d,l,~b,h) + P(d,~l,b,h) + P(d,~l,~b,h) + P(d,l,b,~h) + P(d,l,~b,~h) + P(d,~l,b,~h) + P(d,~l,~b,~h)= P(d|l)P(l|h,b)P(b)P(h) + P(d|l)P(l|h,~b)P(~b)P(h) + P(d|~l)P(~l|h,b)P(b)P(h) + P(d|~l)P(~l|h,~b)P(~b)P(h) + P(d|l)P(l|h,b)P(b)P(~h) + P(d|l)P(l|h,~b)P(~b)P(~h) + P(d|~l)P(~l|h,b)P(b)P(~h) + P(d|~l)P(~l|h,~b)P(~b)P(~h)
ΣH P(H) * ΣB P(B) * ΣL P(d|L)P(L|H,B)FH1() FB1(H) FL1(H,B)
ΣH P(H) * ΣL P(d|L) * ΣB P(L|H,B)P(B)FH2() FL2(H) FB2(H,L)
= =
ΣB P(B) * ΣL P(d|L) * ΣH P(L|H,B)P(H)FB3() FL3(B) FH3(B,L)
=
H B
E L
F D
P(b) , P(~b)f(H)
f(E,H)P(l|h,b) P(l|~h,b) P(~l|h,b) P(~l|~h,b)
P(l|h,~b) P(l|~h,~b) P(~l|h,~b) P(~l|~h,~b)
f(d,L) = [P(d|l), P(d|~l)]f(F,E)
f(B)
f(L,h,B)
