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Transcript of Graphical Models - Inference -
Graphical Models- Inference -
Graphical Models- Inference -
Wolfram Burgard, Luc De Raedt, Kristian Kersting, Bernhard Nebel
Albert-Ludwigs University Freiburg, Germany
PCWP CO
HRBP
HREKG HRSAT
ERRCAUTERHRHISTORY
CATECHOL
SAO2 EXPCO2
ARTCO2
VENTALV
VENTLUNG VENITUBE
DISCONNECT
MINVOLSET
VENTMACHKINKEDTUBEINTUBATIONPULMEMBOLUS
PAP SHUNT
ANAPHYLAXIS
MINOVL
PVSAT
FIO2PRESS
INSUFFANESTHTPR
LVFAILURE
ERRBLOWOUTPUTSTROEVOLUMELVEDVOLUME
HYPOVOLEMIA
CVP
BP
Mainly based on F. V. Jensen, „Bayesian Networks and Decision Graphs“, Springer-Verlag New York, 2001.
AdvancedI WS 06/07
Most Probable Explanation
Bayesian Networks
Bayesian Networks
AdvancedI WS 06/07 Outline
• Introduction • Reminder: Probability theory• Basics of Bayesian Networks• Modeling Bayesian networks• Inference (VE, Junction
tree,MPE)• Excourse: Markov Networks• Learning Bayesian networks• Relational Models
Bayesian Networks
Bayesian Networks
AdvancedI WS 06/07
∑∏b
Elimination operator
P(a|e=0)
factor B:
P(a)
P(c|a)
P(b|a) P(d|b,a) P(e|b,c)
facotr C:
factor D:
factor E:
factor A:
e=0
B
C
D
E
A
e)(a,hD
(a)hE
e)c,d,(a,hB
e)d,(a,hC
VE, Bucket elimination [Dechter ‘96]
- Inference (MPE)
- Inference (MPE)
Bayesian Networks
Bayesian Networks
AdvancedI WS 06/07
Finding MPE [Dechter ‘96]
∏b
maxElimination operator
MPE
factor B:
P(a)
P(c|a)
P(b|a) P(d|b,a) P(e|b,c)
factor C:
factor D:
factor E:
factor A:
e=0
B
C
D
E
A
e)(a,hD
(a)hE
e)c,d,(a,hB
e)d,(a,hC
)xP(maxMPEx
=
),|(),|()|()|()(maxby replaced is
,,,,cbePbadPabPacPaPMPE
:
bcdea=
∑ max
- Inference (MPE)
- Inference (MPE)
Bayesian Networks
Bayesian Networks
AdvancedI WS 06/07 Generating the MPE-tuple
C:
E:
P(b|a) P(d|b,a) P(e|b,c)B:
D:
A: P(a)
P(c|a)
e=0 e)(a,hD
(a)hE
e)c,d,(a,hB
e)d,(a,hC
(a)hP(a)max arga' 1. E
a⋅=
0e' 2. =
)e'd,,(a'hmax argd' 3. C
d=
)e'c,,d',(a'h
)a'|P(cmax argc' 4.B
c
××=
)c'b,|P(e')a'b,|P(d')a'|P(bmax argb' 5.
b××
×=
)e',d',c',b',(a' Return
- Inference (MPE)
- Inference (MPE)