Compensating for Relaxations Arthur Choi Bayesian Networks Reasoning in Bayesian networks artificial intelligence machine learning computer vision information theory statistical physics information retrieval computational biology ID: 934753
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Slide1
Belief Propagation and Approximate Inference: Compensating for Relaxations
Arthur Choi
Slide2Bayesian NetworksReasoning in Bayesian networks:
artificial intelligence, machine learning, computer vision, information theory, statistical physics, information retrieval, computational biology …
This thesis:
develop a perspective on approximate algorithms for inference that:
yields more accuracte and effective approximations
allows us to easily design new
approximations
Slide3Example: Coding
U
0
U
1
U
2
U
3
X0
X
1
X
2
X
3
Y
0
Y'0
Y
1
Y'
1
Y
2
Y'
2
Y
3
Y'
3
X'
0
S
0
X'
1
S
1
X'
2
S
2
X'
3
S
3
Pr
(
U
,
S
,
X
,
Y
) = ∏
i
Pr
(
U
i
)·
Pr
(
X
i
|
U
i
)·
P
r
(
Y
i
|
X
i
)
·
Pr
(
S
i
|
S
i
-1
U
i
)·
Pr
(
X'
i
|
S
i
)·
P
r
(
Y'
i
|
X'
i
)
Slide4Example: Coding
U
0
U
1
U
2
U
3
X
0
X
1
X
2
X
3
Y
0
Y'0
Y
1
Y'
1
Y
2
Y'
2
Y
3
Y'
3
X'
0
S
0
X'
1
S
1
X'
2
S
2
X'
3
S
3
Pr
(
U
,
S
,
X
,
Y
) = ∏
i
Pr
(
U
i
)·
Pr
(
X
i
|
U
i
)·
P
r
(
Y
i
|
X
i
)
·
Pr
(
S
i
|
S
i
-1
U
i
)·
Pr
(
X'
i
|
S
i
)·
Pr(Y'i|X'i)
Slide5Example: Coding
U
0
U
1
U
2
U
3
X0
X
1
X
2
X
3
Y
0
Y'0
Y
1
Y'
1
Y
2
Y'
2
Y
3
Y'
3
X'
0
S
0
X'
1
S
1
X'
2
S
2
X'
3
S
3
Query:
argmax
{
Pr
(
U
i
=0 |
y
),
Pr
(
U
i
=1 |
y
) }
Slide6Treewidth
Slide7Main Idea
Given model
M
Slide8Main Idea
Given model
M
Relax the model
Slide9Main Idea
Given model
M
Relax the model
Reason insimpler model
?
?
Slide10Main Idea
Given model
M
Relax the model
Reason in
simpler model
Compensate
Slide11Main Idea
Given model
M
Relax the model
Reason in
simpler model
Compensate
Reason inimproved model
?
?
Slide12Main Idea
Given model
M
Relax the model
Reason in
simpler model
CompensateReason in
improved modelRecover
Slide13Main Idea
Given model
M
Relax the model
Reason in
simpler model
CompensateReason in
improved modelRecover
Generic approach: use in Bayes nets,
probabilistic graphical models, SAT, etc.
Slide14Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
Compensate for relaxation:
Restore a weaker equivalence
Recover structure, identify
an improved approximation
Slide15Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
Compensate for relaxation:
Restore a weaker equivalence
Recover structure, identify
an improved approximation
Slide16Probabilistic Graphical Models
Bayesian Network:
Pr
(
x
)
= ∏xu Pr(x
|u) =
∏xu θx|
uMarkov Network (or factor graph): Pr(
x) = Z-1
·∏aψa(x
a)
Z = ∑
x∏aψ
a(xa)
A
CB
DFE
G
I
H
Slide17Probabilistic Queries
Pr
(
x
) =
Z
-1·∏aψa
(xa)MAP explanations:
x* = argmaxx
Pr(x) = argmaxx ∏
aψa
(xa)Partition function: Z
=
∑x ∏a
ψa
(xa)
A
CB
DFE
G
I
H
Slide18Probabilistic Queries
Pr
(
x
) =
Z
-1·∏aψa
(xa)Marginals:
Pr(X=x
) =
Z-1·
∑x:X=x
∏aψ
a(xa)
A
C
B
DF
EG
I
H
Slide19Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
Compensate for relaxation:
Restore a weaker equivalence
Recover structure, identify
an improved approximation
Slide20Relax: Treewidth
Slide21Relax Equivalence Constraints
Equivalence constraint:
ψ
eq
(
Xi=x
i,Xj=x
j) = 1 if xi
= xj 0 otherwise
A
C
B
D
F
E
G
I
H
Slide22Relaxing Equivalence Constraints
Model
M
A
B
C
D
E
F
G
H
I
Slide23Relaxing Equivalence Constraints
Model + Eq.
A
B
C
1
D
E
1
F
G
H
1
I
1
E
2
Slide24Relaxing Equivalence Constraints
Model + Eq.
A
B
C
1
D
E
1
F
G
H
1
I
1
C
2
E
2
I
2
H2
Slide25Relaxing Equivalence Constraints
Relaxed
Treewidth 1
A
B
C
1
D
E
1
F
G
H
1
I
1
C
2
E2I2H2
Slide26Relaxing Equivalence Constraints
Model
M
A
B
C
D
E
F
G
H
I
Slide27Relaxing Equivalence Constraints
Model + Eq.
A
B
C
1
D
E
1
G
1
C
2
E
2
F
G
2HI
Slide28Relaxing Equivalence Constraints
Relaxed
Decomposed
A
B
C
1
D
E
1
G
1
C
2
E
2
F
G2HI
Slide29Relaxing Equivalence Constraints
MAP in original model (with eq. constraints):
MAP = max
x
∏
aψa(x
a) · ∏ijψ
eq(Xi=x
i,Xj=
xj)
MAP in relaxed model: r-MAP = maxx ∏aψ
a(xa
) ≥ MAP
Slide30Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
Compensate for relaxation:
Restore a weaker equivalence
Recover structure, identify
an improved approximation
Slide31Relaxation
[
Choi, Chavira & Darwiche UAI-07
]
Mini-buckets algorithm
:Approximation algorithm on exact model, equivalent to exact algorithm on relaxed modelBranch-and-bound depth-first search
Identify new properties of approximationReduce size of search spaceDesign mini-bucket approximationsUse better exact algorithms on relaxed model
Slide32Relaxation: Search Space
x
1
x
s
x
2
x
s
+1
xn
Deeper Search
Size:
|
X
|
s
Size: |X|nReducedSpaceFullSearch Space
Slide33Relaxation: Better Inference
Approximate inference as exact inference in a simplified model
Use state-of-the-art exact algorithms
X
Y
Z
Factorization
Better Factorization
Slide34Empirical Impications
Search
AC
MB
Relative
Network
Nodes
Time (s)
Time (s)
Improvement
90-20-1
14985
18
2417
135
90-20-2
137783
111
15953
144
90-20-3
3065
4
1271
334
90-20-4
4545
3
988
355
90-20-5
29343
38
6579
173
90-20-6
5065
3
630
227
90-20-7
2987
2
1155
485
90-20-8
6213
6
812
146
90-20-9
5121
5
2367
480
90-20-10
8419
10
2343
235
Slide35Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
Compensate for relaxation:
Restore a weaker equivalence
Recover structure, identify
an improved approximation
Slide36Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
A new semantics for BP
marginals
partition function
MAP
Ideal compensations
Recover structure, identify
an improved approximation
Slide37Belief Propagation
Slide38Belief Propagation
Slide39Belief Propagation:What if there are loops?
Slide40Application: Information Theory
Slide41Application: Information Theory
Turbo
Codes, LDPC Code
Berrou
, Glavieux 1993
Mackay
, Neal 1995 (Gallager 1962)Decoding is loopy belief propagation in BNMcEliece, MacKay, Chang 1998“A revolution: BP in graphs with cycles”Frey, MacKay 1998
Slide42Larger Shift
Closer Object
Smaller Shift
Further Object
Slide43Output: Depth Map
Slide44Input: L&R Image
Output: Depth Map
Markov Network
Images Define a
Markov Network
Reasoning in
Markov Network
Estimates Depth
Slide45Stereo Vision
http://vision.middlebury.edu/stereo/eval/
Top 7 highest ranking are
loopy BP or extend loopy BP
Slide46Application: Satisfiability
Survey Propagation:
Surprisingly effective for random k-SAT
SP good up to
α
= 4.23 < 4.26 critical threshold
Slide47Previously …Previously, on edge deletion …
[
Choi, Chan & Darwiche UAI-05
]
Approximate inference by edge deletion
[Choi & Darwiche UAI-06]:
A variational approach: minimize KL-divergence[Choi & Darwiche AAAI-06]:An edge deletion semantics for belief propagationmarginal approximations
Slide48Deleting an Equivalence Edge
X
i
X
j
Slide49Deleting an Equivalence Edge
X
i
X
j
Slide50Deleting an Equivalence Edge
X
i
X
j
Slide51Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
A new semantics for BP
marginals
partition function
MAP
Ideal compensations
Recover structure, identify
an improved approximation
Slide52Deleting an Equivalence Edge
X
i
X
j
Restore a
weaker notion of equivalence
:
[
Choi
& Darwiche
AAAI-06
]
Slide53Parametrizing Edges Iteratively: ED-BP
Iteration
t
= 0
Initialization
Slide54Parametrizing Edges Iteratively: ED-BP
Iteration
t
= 1
Slide55Parametrizing Edges Iteratively: ED-BP
Iteration
t
= 2
Slide56Parametrizing Edges Iteratively: ED-BP
Iteration
t
Convergence
Slide57Belief Propagation as Edge Deletion
Iteration
t
Iteration
t
Slide58BP is a disconnected approximation.
BP is
any
polytree approximation.
Deleting Edges and
Loopy
Belief Propagation
BP in a
network
.
[
Choi
& Darwiche
AAAI-06
]
Slide59A New Semantics for Belief Propagation
ED-BP networks
:
[
Choi
& Darwiche
AAAI-06
]
Slide60A New Semantics for Belief Propagation
Loopy BP
marginals
ED-BP networks
:
[
Choi
& Darwiche
AAAI-06
]
Slide61A New Semantics for Belief Propagation
Loopy BP
marginals
Exact
Inference
ED-BP networks
:
[
Choi
& Darwiche
AAAI-06
]
Slide62Model + Eq
Relax
Compensate/
Correct
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
A
new semantics for BP
marginals
partition function
MAP
Ideal compensations
Recover structure, identify
an improved approximation
Slide63Relaxing Equivalence Constraints
In original model (with eq. constraints):
Pr
(
x
) = Z-1·∏a
ψa(xa) ·
∏ijψeq(X
i=xi,X
j=xj
) Z = ∑x ∏
aψa
(xa) · ∏ij
ψeq(
Xi=xi,X
j=x
j)In relaxed model: Z0 = ∑x ∏aψa(xa)In compensated model: Z' = ∑
x ∏aψa(xa) · ∏ijθ(Xi=xi)θ
(Xj
=xj
)
Slide64Deleting an Equivalence Edge
X
i
X
j
Restore a
weaker notion of equivalence
:
[
Choi
&
Darwiche
UAI-08
]
Slide65Prop.:
If
MI
(
X
i,Xj
) = 0 in ED-BP network M', then:
whereAn Easy Case: Delete a Single Edge
X
i
X
j
With multiple edges deleted
(
ZERO-EC
):
[
Choi
&
Darwiche
UAI-08]
Slide66Prop.:
For any edge in
ED-BP network
M
'
:where
An Easy Case: Delete a Single Edge
X
i
X
j
With multiple edges deleted
(
GENERAL-EC
):
[
Choi
&
Darwiche
UAI-08
]
Slide67Bethe free energy approximation:
as a partition function approximation:
Bethe Free Energy is
ZERO-EC
Theorem:
The Bethe approximation
is ZERO-EC when
M'
is a tree :
M
M'
[
Choi
&
Darwiche
UAI-08
]
Slide68Overview
tree
exact
marginals
zero-EC
general-EC
LBP
Bethe
IJGP
exact
marginals
exact Z
recover edges
joingraph
free energies
Slide69Edge Correction
0
25
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
edges recovered
relative error
6x6 grid
EC-Z,rand
EC-G,rand
Bethe
exact Z
Slide70Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
A
new semantics for BP
marginals
partition function
MAP
Ideal compensations
Recover structure, identify
an improved approximation
Slide71Compensating for Relaxations
[
Choi & Darwiche NIPS-09
]
Max-product belief propagation as compensation
New approximation based on ideal compensationtighter upper-bounds than a relaxation (empirically)
Slide72Relaxing Equivalence Constraints
In original model (with eq. constraints):
MAP =
max
x
∏aψa(
xa)·∏ijψ
eq(Xi=x
i,Xj=x
j)In relaxed model:
r-MAP = maxx ∏aψ
a(xa
)In compensated model: c-MAP = maxx
∏aψ
a(xa)·∏ijθ
(Xi
=xi)θ(Xj=xj) MAP ≤ c-MAP ≤ r-MAP ?
Slide73Compensation: REC-BP
X
i
X
j
Recover a
weaker notion of equivalence
:
Intuition [REC-BP]:
A compensation should be exact if a model is split into two independent sub-models:
[
Choi
&
Darwiche
NIPS-09
]
Slide74BP is a disconnected approximation.
BP is
any
polytree approximation.
Deleting Edges and
Loopy
Belief Propagation
BP in a Bayesian network.
[
Choi
&
Darwiche
NIPS-09
]
Slide75Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
A
new semantics for BP
marginals
partition function
MAP
Ideal compensations
Recover structure, identify
an improved approximation
Slide76Relaxing Equivalence Constraints
In original model (with eq. constraints):
MAP =
max
x
∏aψa(
xa)·∏ijψ
eq(Xi=x
i,Xj=x
j)In relaxed model:
r-MAP = maxx ∏aψ
a(xa
)In compensated model: c-MAP = maxx
∏aψ
a(xa)·∏ijθ
(Xi
=xi)θ(Xj=xj) MAP ≤ c-MAP ≤ r-MAP ?[Choi & Darwiche
NIPS-09]
Slide77Compensation: Idealized Case
Say we relax a single equivalence constraint…
A
compensation has
valid configurations
if:c-MAP(
Xi=x) = c-MAP
(Xj=x) = c-MAP
(Xi=x,Xj=x)
A compensation has scaled values if:log c-MAP(Xi=x,X
j=x) =
κ · log MAP(Xi=x,X
j=x)
A compensation with valid configurations and scaled values is idealit is as good as having Xi ≡
Xj
[Choi & Darwiche NIPS-09]
Slide78Compensation: REC-I
X
i
X
j
Recover
a
weaker notion of equivalence
:
Intuition [REC-I]:
A compensation should be ideal, i.e., have valid configurations and scaled
values.
Proposition:
If a compensation is ideal, then it recovers the following weaker notion of equivalence.
[
Choi
&
Darwiche
NIPS-09]
Slide79Properties
Proposition 1
: For a single equivalence constraint relaxed:
MAP ≤ c-MAP ≤ r-MAP
Theorem
1
: For any k equivalence constraints relaxed in REC-I:MAP ≤ c-MAP
[Choi & Darwiche NIPS-09]
Slide80Experiments
Set initial parameters so that:
c-MAP
=
r-MAP
Slide81Iterative Dynamics
[
Choi
&
Darwiche
NIPS-09
]
Slide82Iterative Dynamics
[
Choi
&
Darwiche
NIPS-09
]
Slide83Iterative Dynamics
[
Choi
&
Darwiche
NIPS-09
]
Slide84Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
Compensate for relaxation:
Restore a weaker equivalence
Recover structure, identify
an improved approximation
Slide85Which edges do we recover?
A minimal polytree.
A
maximal
polytree:
let
us rank all edges.
Slide86Edge Recovery: ZERO-EC
i
j
Recover edges with largest
MI
(
X
i
;
X
j
)
M
i
M
j
[
Choi
&
Darwiche
UAI-08
]
Slide87Edge Recovery: GENERAL-EC
j
i
t
s
Recover edges with largest
MI
(
X
i
,
X
j
;
X
s
,
X
t
)
M
i
M
j
[
Choi
& Darwiche UAI-08]
Slide88Edge Recovery
0
25
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
edges recovered
relative error
6x6 grid
EC-Z,rand
Bethe
exact Z
[
Choi
&
Darwiche
UAI-08
]
Slide89Edge Recovery
0
25
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
edges recovered
relative error
6x6 grid
EC-Z,rand
EC-G,rand
Bethe
exact Z
[
Choi
&
Darwiche
UAI-08
]
Slide90Edge Recovery
0
25
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
edges recovered
relative error
6x6 grid
EC-Z,rand
EC-G,rand
EC-Z,MI
Bethe
exact Z
[
Choi
&
Darwiche
UAI-08
]
Slide91Edge Recovery
0
25
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
edges recovered
relative error
6x6 grid
EC-Z,rand
EC-G,rand
EC-Z,MI
EC-G,MI
Bethe
exact Z
[
Choi
&
Darwiche
UAI-08
]
Slide92Edge Recovery
0
25
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
edges recovered
relative error
6x6 grid
EC-Z,rand
EC-G,rand
EC-Z,MI
EC-G,MI
EC-G,MI2
Bethe
exact Z
[
Choi
&
Darwiche
UAI-08
]
Slide93Many-Pairs Mutual Information
X
Y
mutual
information
can be
expensive
[
Choi
&
Darwiche
AAAI-08a
]
Slide94Soft d-Separation in Polytrees
W
Sequential
Valve
Theorem 1:
MI
(
X
;
Y
|
z)
ENT(W |
z)
X
W
Y
[
Choi
&
Darwiche AAAI-08a]
Slide95Soft d-Separation in Polytrees
W
Divergent
Valve
Theorem 1:
MI
(
X
;
Y
|
z)
ENT(W | z
)
X
W
Y
[
Choi
&
Darwiche AAAI-08a]
Slide96Soft d-Separation in Polytrees
N
1
W
N
1
Convergent
Valve
Theorem 2:
MI
(
X;Y
| z) MI(
N1
;N2 | z
)
XN1
WN2Y
[
Choi
& Darwiche AAAI-08a]
Slide97Many-Pairs Mutual Information
MI
can be
expensive, even
in
polytreesBayesian network
n variables, at most w parents and s statesOne run of BP: O(ns
w) timesingle pair: MI: O(s) runs of BP, O(s
nsw) timePr(X,Y|z) = Pr(X|Y,z) Pr(
Y|z)sd-sep: one run of BP, O(n + nsw) time
k-pairs:MI: O(ks) runs of BP, O(
ks nsw) timesd-sep: one run of BP, O(kn +
nsw) time
[Choi & Darwiche AAAI-08a]
Slide98Empirical Results
network
method
0%
10%
20%
rank time
# deleted
# params
barley
random
115ms
120ms
141ms
0ms
37
130180
MI
111ms
93ms
2999ms
sd-sep
110ms
125ms
46ms
65.84x
diabetes
random
732ms
1103ms
1651ms
0ms
190
461069
MI
550ms
674ms
84604ms
sd-sep
957ms
1639ms
132ms
641.99x
mildew
random
238ms
241ms
243ms
0ms
12
547158
MI
233ms
263ms
6661ms
sd-sep
245ms
323ms
42ms
157.26x
munin1
random
13ms
14ms
22ms
0ms
94
19466
MI
12ms
10ms
680ms
sd-sep
10ms
10ms
35ms
19.57x
[
Choi
&
Darwiche
AAAI-08a
]
Slide99Empiricial Results
0
152
1
2
3
4
5
x 10
edges recovered
average KL-error
pigs
random
true-MI
sd-sep
[
Choi
&
Darwiche
AAAI-08a
]
Slide100Focusing Approximations
Different queries suggest recovery of different edges
[
Choi
&
Darwiche
AAAI-08b
]
Slide101Focusing Approximations
query node
Different queries suggest recovery of different edges
[
Choi
&
Darwiche
AAAI-08b
]
Slide102Focusing Approximations
query node
Different queries suggest recovery of different edges
[
Choi
&
Darwiche
AAAI-08b
]
Slide103Loopy BP
marginals
Exact
Inference
recover edges
Focusing Approximations
[
Choi
&
Darwiche
AAAI-08b
]
Slide104Model + Eq
Relax
Compensate
Recover
Intractable model, augmented
with equivalence constraints
Simplify network structure:
Relax equivalence constraints
Compensate for relaxation:
Restore a weaker equivalence
Recover structure, identify
an improved approximation
More…
Applied to Max-SAT
Tag-SNP selection
Inference Evaluation
Public implementation: SamIam
Slide105An Application to Max-SAT
[
Choi, Standley & Darwiche CP-09
]:
Compensate for Max-SAT relaxations
[Pipatsrisawat, Palyan, Chavira, Choi & Darwiche JSAT-09]:
Relaxations of Max-SAT problemsdepth-first brand-and-bound search
Slide106Weighted Max-SAT
A
C
B
D
F
E
G
I
H
(
a
b
,
w
1
)
(
¬
a ¬b,w
2)(b c,
w
3)
(¬b ¬c
,w4)(b
¬e
,wa)(¬b
e,wb)…
…
[
Choi, Standley
&
Darwiche
CP-09
]
Slide107Weighted Max-SAT: Equivalence Constraints
Relax an equivalence constraint:
(
X
≡
Y,∞) = {(x
¬y,∞), (¬x
y,∞)}Compensate with unit clauses:
{(x,wx), (
¬x,w
¬x), (y,wy
), (¬y,
w¬y)}How do we set these new weights?
[Choi, Standley & Darwiche
CP-09]
Slide108Weighted Max-SAT: Compensation
A compensation has
valid configurations
if:
G
(
x) = G(y) = G
(x,y)G(
¬x) = G(¬y
) = G(¬x, ¬y
)A compensation has scaled values if: G
(x,y) = κ
· F(
x,y)G(¬x
,¬y) =
κ · F(¬x
,¬y)
A compensation with valid configurations and scaled values is idealit is as good as having X ≡ Y[Choi, Standley & Darwiche CP-09]
Slide109Weighted Max-SAT: Experiments
Tighter upper-bounds: more efficient depth-first branch-and-bound search.
Compensation bounds embedded in Clone
[
Choi, Standley
&
Darwiche
CP-09]
Slide110Application: Biology
[
Choi,Zaitlen,Hahn,Pipatsrisawat,Darwiche&Eskin WABI-08
]:
Optimal tag SNP selection
(s
1
∨ s2)
(s1 ∨ s2 ∨ s3
)(s2 ∨ s
3 ∨ s4 ∨ s
5)…
Slide111Inference Evaluations
UAI-06: participant
UCLA: only group to solve all models for all tasks
UAI-08: participant, co-organizer
ED-BP: leader in multiple benchmarks, for approx PRE and approx MAR tasks
results presented at:UAI-08 conference and workshopCP-08 workshop
NIPS-08 workshop
Slide112Probabilistic Reasoning Evaluation of UAI’08
Evaluation Chairs:
Adnan Darwiche (UCLA)
Rina
Dechter (UCI)Student Organizers:
Arthur Choi (UCLA)Vibhav Gogate (UCI)Lars Otten (UCI)Special Thanks:
Eleazar Eskin (UCLA)Evaluation CommitteeFahiem Bacchus (
UToronto)Jeff Bilmes (UW)Hector Geffner (UPF)Alexander Ihler (UCI)
Joris Mooij (Radboud)Kevin Murphy (UBC)
Slide113Probabilistic Reasoning Evaluation of UAI’08
Scope:
Probability of Evidence (partition function)
Most Probable Explanation (energy minimization)
Node Marginals
Evaluated exact and approximate inference1,181 Bayesian and Markov networks
26 solvers evaluated from 7 groups
Slide114Approx PE Results (Binary)
higher score
faster solver
Slide115Workshop page: http://graphmod.ics.uci.edu/uai08/
Slide116http://reasoning.cs.ucla.edu/samiam/
Slide117Slide118Slide119Slide120Slide121Slide122http://reasoning.cs.ucla.edu
Slide123Arthur
Choi
,
Hei
Chan, and Adnan Darwiche. On Bayesian Network Approximation by Edge Deletion. In Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence (
UAI), 2005.Arthur Choi and Adnan Darwiche. An Edge Deletion Semantics for Belief Propagation and its Practical Impact on Approximation Quality. In Proceedings of the 21st National Conference on Artificial Intelligence (
AAAI), 2006.Arthur Choi and Adnan Darwiche. A Variational Approach for Approximating Bayesian Networks by Edge Deletion. In
Proceedings of the 22nd Conference on Uncertainty in Artificial Intelligence (UAI), 2006.Arthur Choi, Mark Chavira, and Adnan Darwiche. Node Splitting: A Scheme for Generating Upper Bounds in Bayesian Networks. In
Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence (UAI), 2007.Arthur
Choi and Adnan Darwiche. Approximating the Partition Function by Deleting and then Correcting for Model Edges. In Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence (UAI
), 2008.Arthur Choi and Adnan Darwiche. Focusing Generalizations of Belief Propagation on Targeted Queries. In Proceedings of the 23rd AAAI Conference on Artificial Intelligence (AAAI)
, 2008.Arthur Choi and Adnan Darwiche. Many-Pairs Mutual Information for Adding Structure to Belief Propagation Approximations. In
Proceedings of the 23rd AAAI Conference on Artificial Intelligence (AAAI), 2008.Arthur Choi and Adnan Darwiche. Approximating MAP by Compensating for Structural Relaxations. In
Proceedings of the Twenty-Third Annual Conference on Neural Information Processing Systems (NIPS), 2009.
Arthur Choi, Trevor Standley, and Adnan Darwiche. Approximating Weighted Max-SAT Problems by Compensating for Relaxations. In Proceedings of the 15th International Conference on Principles and Practice of Constraint Programming (CP), 2009.
Arthur Choi, Noah Zaitlen,
Buhm Hahn, Knot Pipatsrisawat, Adnan Darwiche, and Eleazar Eskin. Efficient Genome Wide Tagging by Reduction to SAT. In Proceedings of the 8th Workshop on Algorithms in Bioinformatics (WABI), 2008.Knot Pipatsrisawat, Akop Palyan, Mark Chavira, Arthur Choi, and Adnan Darwiche. Solving Weighted Max-SAT Problems in a Reduced Search Space: A Performance Analysis. Journal on Satisfiability Boolean Modeling and Computation (JSAT), 2008.Publications
Slide124Thanks …
David Allen, Kurt Angle, Omer Bar-or, Jeff Bergman, Keith Cascio, Hei Chan, Mark Chavira, Yang Chen, Alex Choy, Rina Dechter, Bailu Ding, Alex Dow, Eleazar Eskin, Kamron Farrokh, Buhm Han, Dan He, Jinbo Huang, Deepak Khosla, Robert Lee, Glen Lenker, Tsai-Ching Lu, Sam Luckenbill, JD Park, Akop Palyan, Knot Pipatsrisawat, Wojtek Przytula, Ethan Schreiber, Grace Shih, Trevor Standley, Sam Talaie, Alan Yuille, Yulia Zabiyaka, Noah Zaitlen
Committee members: Adam Meyerson, Demetri Terzopoulos, Alan Yuille, Jan de Leeuw
… and Adnan Darwiche