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
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Key Results/Publications

• KR02 A logical approach to factoring belief
  networks Adnan Darwiche
• AAAI02 A distance measure for bounding
  probabilistic belief change Hei Chan
  and Adnan Darwiche
• AAAI02 A compiler for deterministic
  decomposable negation normal form
  Adnan Darwiche
• AAAI02 Using weighted MAX-SAT to approximate
  MPE James Park
• UAI02 MAP complexity results and
  approximation methods James Park
• TR-118 A differential semantics for jointree
  algorithms James Park and Adnan
  Darwiche
• TR-130 Optimal time-space tradeoffs in
  probabilistic inference David Allen and
  Adnan Darwiche

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Key Results

• Factoring belief networks for exact inference
• Exact inference with networks of treewidth gt 60
• A new perspective on factoring belief networks
• Bounding probabilistic belief change
• New distance measure
• Applications to sensitivity analysis, belief
  revision and uncertain evidence

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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

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• Maximum Time 430 sec

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Recursive Conditioning
Battery Age
Alternator
Fan Belt
Leak
Charge Delivered
Battery
Fuel Line
Starter
Gas
Distributor
Battery Power
Spark Plugs
Gas Gauge
Engine Start
Lights
Engine Turn Over
Radio
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Case-Analysis
Battery Age
Alternator
Fan Belt
Battery Age
Alternator
Fan Belt
Leak
Leak
Charge Delivered
Charge Delivered
Battery
Fuel Line
Battery
Fuel Line
Starter
Gas
Starter
Distributor
Gas
Distributor
Battery Power
Battery Power
Spark Plugs
Spark Plugs
Gas Gauge
Gas Gauge
Lights
Engine Turn Over
Engine Start
Radio
Lights
Engine Turn Over
Engine Start
Radio
Case I
Case II
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Decomposition
Battery Age
Alternator
Fan Belt
Battery Age
Alternator
Fan Belt
Leak
Leak
Charge Delivered
Charge Delivered
Battery
Fuel Line
Battery
Fuel Line
Starter
Starter
Gas
Distributor
Gas
Distributor
Battery Power
Battery Power
Spark Plugs
Spark Plugs
Gas Gauge
Gas Gauge
Lights
Engine Turn Over
Engine Start
Radio
Lights
Engine Turn Over
Engine Start
Radio
Case I
Case II
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Decomposition
Case I
Case II
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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
Radio
Engine Turn Over
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Decomposition Tree
A
B
C
D
E
B
B
E
D
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Decomposition Tree
A
B
C
D
E
Time O(n2w)
B
Space O(n2w)
B
C
A
E
D
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Time-Space Tradeoffs
64 cache entries
rc(T)cutset(Tp)cf(Tp)context(Tp)(1-cf(Tp))rc(
Tp)
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Results

• Networks
• Barley
• Mildew
• Water
• Random
• Graphs
• Optimal time-space curves
• 8 byte cache values
• 3.5 million calls to RC per second

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• Maximum Time 560 sec Average Time 38.6 sec

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• Maximum Search Time 1.8 sec Average Time 1.3
  sec

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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

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• Maximum Time 430 sec

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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

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Bayesian Network
Pr(LightsON Battery-PowerOK) .99
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Query Types

• Pr Posterior marginals
• MPE Most probable instantiation
• MAP Maximum a posteriori hypothesis

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Pr Posterior Marginals
Battery Age
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Fuel Pump
Fuel Line
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Distributor
Gas
Battery Power
Spark Plugs
Gas Gauge
Lights
Engine Turn Over
Engine Start
Radio
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MPE Most Probable Explanation
Battery Age
Alternator
Fan Belt
Charge Delivered
Battery
Fuel Pump
Fuel Line
Starter
Distributor
Gas
Battery Power
Spark Plugs
Gas Gauge
Lights
Engine Turn Over
Engine Start
Radio
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MPE Most Probable Explanation
Battery Age
Alternator
Fan Belt
Charge Delivered
Battery
Fuel Pump
Fuel Line
Starter
Distributor
Gas
Battery Power
Spark Plugs
Gas Gauge
Lights
Engine Turn Over
Engine Start
Radio
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MAP Maximum a Posteriori Hypothesis
Battery Age
Alternator
Fan Belt
Charge Delivered
Battery
Fuel Pump
Fuel Line
Starter
Distributor
Gas
Battery Power
Spark Plugs
Gas Gauge
Lights
Engine Turn Over
Engine Start
Radio
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MAP Maximum a Posteriori Hypothesis
Battery Age
Alternator
Fan Belt
Charge Delivered
Battery
Fuel Pump
Fuel Line
Starter
Distributor
Gas
Battery Power
Spark Plugs
Gas Gauge
Lights
Engine Turn Over
Engine Start
Radio
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MAP Maximum a Posteriori Hypothesis
Battery Age
Alternator
Fan Belt
Charge Delivered
Battery
Fuel Pump
Fuel Line
Starter
Distributor
Gas
Battery Power
Spark Plugs
Gas Gauge
Lights
Engine Turn Over
Engine Start
Radio
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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

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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.

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Scoring Neighbors using BP
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Experimental Results

• Tested on random networks
• 100 variables, 20-25 map variables, width about
  13.
• Also real world networks
• Pigs
• Barley

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Random Networks
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Barley
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Pigs
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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

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Deterministic Networks
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Big Networks

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

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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

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Pr(Prno) .95
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Pr(Prno) .92
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Key Results/Publications

• KR02 A logical approach to factoring belief
  networks Adnan Darwiche
• AAAI02 A distance measure for bounding
  probabilistic belief change Hei Chan
  and Adnan Darwiche
• AAAI02 A compiler for deterministic
  decomposable negation normal form
  Adnan Darwiche
• AAAI02 Using weighted MAX-SAT to approximate
  MPE James Park
• UAI02 MAP complexity results and
  approximation methods James Park
• TR-118 A differential semantics for jointree
  algorithms James Park and Adnan
  Darwiche
• TR-130 Optimal time-space tradeoffs in
  probabilistic inference David Allen and
  Adnan Darwiche

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