inference in dbns with non-disjoint clustersperso.crans.org/~genest/cff.pdf · 2015. 10. 1. ·...
TRANSCRIPT
![Page 1: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/1.jpg)
Inference in DBNs with non-disjoint clusters
Matthieu Pichené
![Page 2: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/2.jpg)
Introduction
![Page 3: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/3.jpg)
Apoptosis pathway
Mcl1
Mcl1
![Page 4: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/4.jpg)
Method
simulations Analysis
MATHEMATICAL FORMALISM
BIOLOGICAL SYSTEM
![Page 5: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/5.jpg)
Method
![Page 6: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/6.jpg)
Method
![Page 7: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/7.jpg)
Method(Approximate) abstrac1on
of the low level biochemical model
![Page 8: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/8.jpg)
DBNs
ES
S
E
P
S + E <—> ES —> P + E
t0 t1 t2 t3
k+1
k-1
k+2
{1 2 3 4 5
{1 2 3 4 5
{1 2 3 4 5
{1 2 3 4 5
Every specie at time point t is a random
variable over a discrete
number of values.
Number of configurations at each time point: ValuesSpecies
![Page 9: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/9.jpg)
DBNs
ES
S
E
P
t0 t1 t2 t3
+CPT
S ES
E P
k+1
k-1
k+2S + E <—> ES —> P + E
![Page 10: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/10.jpg)
CPTS + E <—> ES —> P + Ek+1
k-1
k+2
S S E ES Pr1 1 1 1 0.11 2 1 2 0.22 2 3 3 0.1…
SES S E ES P Pr112…
E S E ES Pr112…
P ES P Pr112…
ES
E P
![Page 11: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/11.jpg)
DBNs
ES
S
E
P
t0 t1 t2 t3
+CPT
S ES
E P
k+1
k-1
k+2S + E <—> ES —> P + E
Complexity of exact inference: at least ValuesSpecies
![Page 12: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/12.jpg)
DBNs
• We need an approximation. Express configurations as product of probabilities
• Simplest idea : Consider all species independent ( Factored Frontier )
![Page 13: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/13.jpg)
Factored Frontier
ES
S
E
P
t0 t1 t2 t3
k+1
k-1
k+2
Hypothesis : Independent
S + E <—> ES —> P + E
complexity of FF inference: Species x ValuesNbPar+1
Pt2(P=h)= f(Pt1(P),Pt1(ES),CPT)
Low accuracy
![Page 14: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/14.jpg)
Clustered Factored Frontier
• Use of clusters containing the species that have the most mutual information
• Clusters may vary over time
• All sets of states for species in a clusters are calculated (that limits the length of clusters)
![Page 15: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/15.jpg)
Clustered Factored Frontier
• Use information theory (Eric) to obtain the important relations
• We (Eric) chose the tree to minimize distance
• Tree implies cluster of size 2
![Page 16: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/16.jpg)
R
R
L:R
L:R
R*
R*
R*:pC8
R
*:pC
8
C8
C8
Bar
Bar
Bid
Bid
C8:Bar
C
8:Ba
r
flip
flip
R*:flip
R
*:flip
pC8
pC8
pC3
pC3
C8:pC3
C
8:pC
3
C3:XIAP
C
3:XI
AP
C3U
C3 U
tBid:Mcl1
tBid
:Mcl
1
C8:Bid
C
8:Bi
d
tBid
tBid
C3
C3
XIAP
XIAP
Smac
Smac
Smacr
S
mac
r
Apop
Apop
Apop:XIAP
Apo
p:XI
AP
PARP
PAR
P
cPARP
cPAR
P
CyCm
CyC
m
Smacm
Smac
m
CyC
CyC
CyCr
CyC
r
Smac:XIAP
Sm
ac:X
IAP
Bax2:Bcl2
Bax
2:Bc
l2
Bcl2
Bcl2
Bax
Bax
Bax*m
Bax*
m
Bax*
Bax*
Bax2
Bax2
Mcl1
Mcl
1
Pore*
Pore
*
Bax4
Bax4
Bax4:M
B
ax4:
M
Bax*m:Bcl2
Bax*
m:B
cl2
Apaf*
A
paf*
pC9
pC
9
Apaf
Apaf
Bax4:Bcl2
Bax
4:Bc
l2
Apop:pC3
Apo
p:pC
3
C3:PARP
C
3:PA
RP
tBid:Bax
tBi
d:Ba
x
M*:CyCm
M
*:CyC
m
M*:Smacm
M*:S
mac
m
CyC:Apaf
CyC
:Apa
f
pC6
pC6
Pore
Pore
C6
C6
C3:pC6
C
3:pC
6
C6:pC8
C
6:pC
8
136 238 5 61439 337 4 7404335464515 8113029345612132528272657492217191820162421514832333150554447525354 923104142
136 238 5 61439 337 4 7404335464515 8113029345612132528272657492217191820162421514832333150554447525354 923104142 0
0.5
1
1.5
2
2.5
3
Mutual information on the whole graph
Mutual Information on the Tree Approximation
R
R
L:R
L:R
R*
R*
R*:pC8
R
*:pC
8
C8
C8
Bar
Bar
Bid
Bid
C8:Bar
C
8:Ba
r
flip
flip
R*:flip
R
*:flip
pC8
pC8
pC3
pC3
C8:pC3
C
8:pC
3
C3:XIAP
C
3:XI
AP
C3U
C3 U
tBid:Mcl1
tBid
:Mcl
1
C8:Bid
C
8:Bi
d
tBid
tBid
C3
C3
XIAP
XIAP
Smac
Smac
Smacr
S
mac
r
Apop
Apop
Apop:XIAP
Apo
p:XI
AP
PARP
PAR
P
cPARP
cPAR
P
CyCm
CyC
m
Smacm
Smac
m
CyC
CyC
CyCr
CyC
r
Smac:XIAP
Sm
ac:X
IAP
Bax2:Bcl2
Bax
2:Bc
l2
Bcl2
Bcl2
Bax
Bax
Bax*m
Bax*
m
Bax*
Bax*
Bax2
Bax2
Mcl1
Mcl
1
Pore*
Pore
*
Bax4
Bax4
Bax4:M
B
ax4:
M
Bax*m:Bcl2
Bax*
m:B
cl2
Apaf*
A
paf*
pC9
pC
9
Apaf
Apaf
Bax4:Bcl2
Bax
4:Bc
l2
Apop:pC3
Apo
p:pC
3
C3:PARP
C
3:PA
RP
tBid:Bax
tBi
d:Ba
x
M*:CyCm
M
*:CyC
m
M*:Smacm
M*:S
mac
m
CyC:Apaf
CyC
:Apa
f
pC6
pC6
Pore
Pore
C6
C6
C3:pC6
C
3:pC
6
C6:pC8
C
6:pC
8
136 238 5 61439 337 4 7404335464515 8113029345612132528272657492217191820162421514832333150554447525354 923104142
136 238 5 61439 337 4 7404335464515 8113029345612132528272657492217191820162421514832333150554447525354 923104142 0
0.5
1
1.5
2
2.5
3
Species correlations (Eric)
![Page 17: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/17.jpg)
Hypothesis :
Pr(St=h,ESt=l,Et=m,Pt=h) =
Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h)
Pr2(ESt=l)
S ES E
P
Clustered Factored Frontierwe assume that relations not in tree are irrelevant
![Page 18: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/18.jpg)
Apoptosis pathway
−1.5 −1 −0.5 0 0.5 1 1.5
−1.5
−1
−0.5
0
0.5
1
1.5
1
R
2
R*
3flip
4 pC8
5
C8
6
Bar
7 pC3
8 C3
9
pC6 10
C6
11XIAP
12
PARP
13
cPARP
14
Bid
15
tBid
16
Mcl1
17
Bax
18
Bax*
19
Bax*
m
20
Bax2
21Bax4
22
Bcl2
23
Pore
24
Pore*
25
CyCm
26
CyC
r
27
CyC
28
Smacm
29 Smacr
30 Smac
31 Apaf
32 Apaf*
33 pC9
34 Apop
35 C3U
36
L:R
37 R
*:flip
38
R
*:pC8
39
C8:Bar
40 C8:pC3
41
C3:pC6
42
C6:pC
8
43 C3:XIAP
44
C3:PARP
45 C8:Bid
46 tBid:Mcl1
47
tBid:Bax
48Bax*m:Bcl2
49
Bax
2:Bc
l2
50
Bax4:Bcl2
51 Bax4:M
52
M*:CyCm53
M*:Smacm54
CyC:Apaf
55
Apop:pC3
56
Apop:XIAP57
Sm
ac:X
IAP
![Page 19: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/19.jpg)
Apoptosis pathway
![Page 20: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/20.jpg)
Clustered Factored Frontier
ES
S
E
P
t0 t1 t2 t3
+CPT
S ES
E P
k+1
k-1
k+2S + E <—> ES —> P + E
![Page 21: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/21.jpg)
Clustered Factored Frontier
ES
S
E
P
t0 t1 t2 t3
+CPT
S ES
E P
k+1
k-1
k+2S + E <—> ES —> P + E
Pt1(s’,es’)=Σs,es,e (Pt0(s,es,e)CPT(s,es,e,s’)CPT(s,es,e,es’))
![Page 22: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/22.jpg)
How our algorithm work
Hypothesis :
Pr(St=h,ESt=l,Et=m,Pt=h) =
Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h)
Pr2(ESt=l)
S ES E
P
![Page 23: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/23.jpg)
How to compute P(parents(Cluster))
Proposition : P(Xp = vp, XL = VL, XR =VR) = P(Xp = vp, XL = VL) x P(Xp = vp, XR =VR)
P(Xp = vp)
p
L R
![Page 24: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/24.jpg)
How to compute P(parents(Cluster))
Parent_Cluster= set of nodes necessary to use the CPTs.
![Page 25: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/25.jpg)
How to compute P(parents(Cluster))
![Page 26: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/26.jpg)
How to compute P(parents(Cluster))
![Page 27: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/27.jpg)
How to compute P(parents(Cluster))
![Page 28: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/28.jpg)
How to compute P(parents(Cluster))
![Page 29: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/29.jpg)
How to compute P(parents(Cluster))
Independence between trees Complexity : Species x Values Parents_Cluster+1
![Page 30: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/30.jpg)
Algorithm comparison
FF ClusteredFF Exact computation
Complexity Species x ValuesNbParents
Species x ValuesParents_Cluster+1 > ValuesSpecies
Accuracy Low ? but better than FF Exact
![Page 31: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/31.jpg)
Conclusion
• Our program is currently still being written. Results will tell if the accuracy is good or not.
• After the first results are obtained we will upgrade it to accept bigger clusters and non-tree graphs
![Page 32: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/32.jpg)
How our algorithm work
![Page 33: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/33.jpg)
How our algorithm work
![Page 34: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/34.jpg)
How our algorithm work
![Page 35: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/35.jpg)
How our algorithm work
![Page 36: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/36.jpg)
How our algorithm work
Order S x N
![Page 37: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/37.jpg)
How our algorithm work
• For each time T groups of clusters are found
• Most efficient path is found to calculate each cluster
• Calculate probability using CPTs
• Results are saved, cluster probabilities are kept in memory
![Page 38: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/38.jpg)
Clustered Factored Frontier
A
A*
A <—> A* CPT:
96.04% A = h , A* = l 0.04% A = l , A* = h 1.96% A = h , A* = h 1.96% A = l , A* = l 0.04% A = h , A* = l 96.04% A = l , A* = h 1.96% A = h , A* = h 1.96% A = l , A* = l
98% : A = h A* = l —> A = h 2% : A = h A* = l —> A = l 2% : A = l A* = h —> A = h 98% : A = l A* = h —> A = l 2% : A = h A* = l —> A* = h 98% : A = h A* = l —> A* = l 98% : A = l A* = h —> A* = h 2% : A = l A* = h —> A* = l
50% A = h A* = l 50% A = l A* = h :
![Page 39: Inference in DBNs with non-disjoint clustersperso.crans.org/~genest/CFF.pdf · 2015. 10. 1. · Pr(St=h,ESt=l) Pr(ESt=l, Et=m) Pr(ESt=l,Pt=h) Pr2(ESt=l) S ES E P Clustered Factored](https://reader034.vdocument.in/reader034/viewer/2022051907/5ffa1e7d1626781e9e715b0f/html5/thumbnails/39.jpg)
Clustered Factored Frontier
A
A*
A <—> A* CPT:
53.04% A = h , A* = l 53.04% A = l , A* = h 1.96% A = h , A* = h 1.96% A = l , A* = l
98% : A = h A* = l —> A = h 2% : A = h A* = l —> A = l 2% : A = l A* = h —> A = h 98% : A = l A* = h —> A = l 2% : A = h A* = l —> A* = h 98% : A = h A* = l —> A* = l 98% : A = l A* = h —> A* = h 2% : A = l A* = h —> A* = l
50% A = h A* = l 50% A = l A* = h :