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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

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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 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

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 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


Maximum Time: 430 sec


Recursive Conditioning

Battery Age

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Case-Analysis

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Battery Power

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Engine Start

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Lights

Engine Start

Engine Turn Over

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Case I

Case II


Decomposition

Battery Age

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Battery Age

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Leak

Leak

Charge Delivered

Charge Delivered

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Battery Power

Spark Plugs

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Engine Start

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Lights

Engine Start

Engine Turn Over

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Case I

Case II


Battery Age

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Battery Age

Alternator

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Leak

Leak

Charge Delivered

Charge Delivered

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Gas

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Battery Power

Spark Plugs

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Spark Plugs

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Engine Start

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Lights

Engine Start

Engine Turn Over

Radio

Decomposition

Case I

Case II


Recursive Decomposition

Battery Age

Alternator

Fan Belt

Leak

Charge Delivered

Battery

Fuel Line

Starter

Gas

Distributor

Battery Power

Spark Plugs

Gas Gauge

Lights

Engine Start

Engine Turn Over

Radio


A

B

B

C

A

C

D

Decomposition Tree

A

B

C

D

E

B

B

E

D


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

  • Networks

    • Barley

    • Mildew

    • Water

    • Random

  • Graphs

    • Optimal time-space curves

    • 8 byte cache values

    • 3.5 million calls to RC per second


Maximum Time: 560 sec Average Time: 38.6 sec


Maximum Search Time: 1.8 sec Average Time: 1.3 sec


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


Maximum Time: 430 sec


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


Battery Age

Alternator

Fan Belt

Charge Delivered

.99

Battery

Fuel Pump

Fuel Line

Starter

Lights

Distributor

Gas

ON

OFF

Battery Power

OK

Spark Plugs

.99

.01

Gas Gauge

Battery Power

.80

.20

WEAK

0

1

DEAD

Engine Start

Lights

Engine Turn Over

Radio

Bayesian Network

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


Query Types

  • Pr: Posterior marginals

  • MPE: Most probable instantiation

  • MAP: Maximum a posteriori hypothesis


Pr: Posterior Marginals

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MPE: Most Probable Explanation

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MPE: Most Probable Explanation

Battery Age

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MAP: Maximum a Posteriori Hypothesis

Battery Age

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MAP: Maximum a Posteriori Hypothesis

Battery Age

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MAP: Maximum a Posteriori Hypothesis

Battery Age

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Charge Delivered

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Fuel Line

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Gas

Battery Power

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Engine Start

Lights

Engine Turn Over

Radio


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

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

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


Scoring Neighbors using BP


Experimental Results

  • Tested on random networks

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

  • Also real world networks

    • Pigs

    • Barley


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


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

  • 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


Deterministic Networks


Big Networks

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


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


Pr(Pr=no) = .95


Pr(Pr=no) = .92


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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