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Automated Reasoning Group. PI: Adnan Darwiche, UCLA http://www.cs.ucla.edu/~darwiche Collaborators: David Allen Keith Cascio Hei Chan James Park. Key Results/Publications. KR’02: A logical approach to factoring belief networks Adnan Darwiche

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Automated reasoning group

Automated Reasoning Group

PI:

Adnan Darwiche, UCLA

http://www.cs.ucla.edu/~darwiche

Collaborators:

David Allen

Keith Cascio

Hei Chan

James Park


Key results publications
Key Results/Publications

KR’02: A logical approach to factoring belief networksAdnan Darwiche

AAAI’02: A distance measure for bounding probabilistic belief changeHei Chan and Adnan Darwiche

AAAI’02: A compiler for deterministic decomposable negation normal formAdnan Darwiche

AAAI’02: Using weighted MAX-SAT to approximate MPEJames Park

UAI’02: MAP complexity results and approximation methodsJames Park

TR-118: A differential semantics for jointree algorithmsJames Park and Adnan Darwiche

TR-130: Optimal time-space tradeoffs in probabilistic inferenceDavid Allen and Adnan Darwiche


Key results
Key Results

Factoring belief networks for exact inference:

  • Exact inference with networks of treewidth > 60

  • A new perspective on factoring belief networks

    Bounding probabilistic belief change:

  • New distance measure

  • Applications to sensitivity analysis, belief revision and uncertain evidence


Key results1
Key Results

MAP/MPE advances:

  • New complexity results

  • Most efficient MAP/MPE engines

    Time-Space tradeoffs:

  • Optimal utilization of space given time constraints

  • Time-space tradeoff curves for real-world networks

    SamIam Demo:

  • Sensitivity engine

  • MAP/MPE

  • Time-Space tradeoffs



Recursive conditioning
Recursive Conditioning

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Case analysis
Case-Analysis

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Case I

Case II


Decomposition
Decomposition

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Case I

Case II


Decomposition1

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Battery Power

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Decomposition

Case I

Case II


Recursive decomposition
Recursive Decomposition

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Decomposition tree

A

B

B

C

A

C

D

Decomposition Tree

A

B

C

D

E

B

B

E

D


Decomposition tree1

Time: O(n2w log n)

Space: O(n)

A

C

D

Decomposition Tree

A

B

C

D

E

Time: O(n2w)

B

Space: O(n2w)

B

C

A

E

D


16

128

8

64

512

8

1024

32

1728 cache entries

Time-Space Tradeoffs

64 cache entries

rc(T)=cutset#(Tp)[cf(Tp)context#(Tp)+(1-cf(Tp))rc(Tp)]


Results
Results

  • Networks

    • Barley

    • Mildew

    • Water

    • Random

  • Graphs

    • Optimal time-space curves

    • 8 byte cache values

    • 3.5 million calls to RC per second




Random network
Random Network

  • 40 nodes, 86 edges, width of 14 (non-binary nodes)

  • Full Caching would require 767 MB

  • Netica cannot compile network: needs ~6 GB

  • Hugin cannot compile network: needs ~11 GB



Key results2
Key Results

MAP/MPE advances:

  • New complexity results

  • Most efficient MAP/MPE engines

    Time-Space tradeoffs:

  • Optimal utilization of space given time constraints

  • Time-space tradeoff curves for real-world networks

    SamIam Demo:

  • Sensitivity engine

  • MAP/MPE

  • Time-Space tradeoffs


Bayesian network

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.99

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.01

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.80

.20

WEAK

0

1

DEAD

Engine Start

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Bayesian Network

Pr(Lights=ON | Battery-Power=OK) = .99


Query types
Query Types

  • Pr: Posterior marginals

  • MPE: Most probable instantiation

  • MAP: Maximum a posteriori hypothesis


Pr posterior marginals
Pr: Posterior Marginals

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MPE: Most Probable Explanation

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MPE: Most Probable Explanation

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Map maximum a posteriori hypothesis
MAP: Maximum a Posteriori Hypothesis

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Map maximum a posteriori hypothesis1
MAP: Maximum a Posteriori Hypothesis

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Map maximum a posteriori hypothesis2
MAP: Maximum a Posteriori Hypothesis

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Complexity results
Complexity Results

  • MPE is effectively an optimization problem

    • MPE is NP-complete

    • MPE is usually solved using counting algorithms!

  • Pr is effectively a counting problem

    • Pr is PP-complete (Roth 96)

  • MAP requires both optimization and counting

    • MAP is NPPP-complete

    • MAP is NP-complete for polytrees

  • NP PP NPPP PHNPPP


Local search bp
Local Search +BP

  • Previous work focused on: local search + exact inferenceApplicable when inference is tractable.

  • Local search + approximate inference (BP)Both optimization and inference problems are intractable.



Experimental results
Experimental Results

  • Tested on random networks

    • 100 variables, 20-25 map variables, width about 13.

  • Also real world networks

    • Pigs

    • Barley


Random networks

Method

# solved Exactly of 59

Worst found/actual

MPE

9

.015

MPE-Hill

41

.06

MPE-Shill

43

.21

ML

31

.34

ML-Hill

38

.46

ML-Shill

42

.72

Random Networks


Barley

Min

Median

Mean

Max

MPE-Hill

1

8.4

1.3x1011

3.1x1012

MPE-SHill

1

8.4

1.3x1011

3.1x1012

ML-Hill

1.0x104

3.6x107

3.4x1015

8.4x1016

ML-SHill

7.7x103

3.6x107

3.4x1015

8.4x1016

Barley


Method

Min

Median

Mean

Max

MPE-Hill

1.0

1.7x105

1.5x107

3.3x108

MPE-SHill

1.0

2.5x105

4.5x1011

1.1x1013

ML-Hill

13.0

2.0x103

3.3x105

4.5x106

ML-SHill

13.0

1.2x104

8.2x105

8.2x106

Pigs


Reducing mpe to maxsat
Reducing MPE to MAXSAT

  • MPE can be reduced to MAXSAT

  • Compared 3 algorithms:

    • Discrete Lagrangian Multipliers (DLM):MAXSAT algorithm

    • Guided Local Search (GLS):MAXSAT algorithm

    • Stochastic Local Search (SLS):A direct MPE solution technique based on stochastic local search



Big networks
Big Networks

  • The third set is not amenable to exact solution so we compare relative solution quality


Key results3
Key Results

MAP/MPE advances:

  • New complexity results

  • Most efficient MAP/MPE engines

    Time-Space tradeoffs:

  • Optimal utilization of space given time constraints

  • Time-space tradeoff curves for real-world networks

    SamIam Demo:

  • Sensitivity engine

  • MAP/MPE

  • Time-Space tradeoffs




Key results publications1
Key Results/Publications

KR’02: A logical approach to factoring belief networksAdnan Darwiche

AAAI’02: A distance measure for bounding probabilistic belief changeHei Chan and Adnan Darwiche

AAAI’02: A compiler for deterministic decomposable negation normal formAdnan Darwiche

AAAI’02: Using weighted MAX-SAT to approximate MPEJames Park

UAI’02: MAP complexity results and approximation methodsJames Park

TR-118: A differential semantics for jointree algorithmsJames Park and Adnan Darwiche

TR-130: Optimal time-space tradeoffs in probabilistic inferenceDavid Allen and Adnan Darwiche


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