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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. KR’02: A logical approach to factoring belief networks Adnan Darwiche

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Automated Reasoning Group

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  1. Automated Reasoning Group PI: Adnan Darwiche, UCLA http://www.cs.ucla.edu/~darwiche Collaborators: David Allen Keith Cascio Hei Chan James Park

  2. 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

  3. 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

  4. 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

  5. Maximum Time: 430 sec

  6. 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

  7. 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 Starter Gas Distributor Gas Distributor Battery Power Battery Power Spark Plugs Spark Plugs Gas Gauge Gas Gauge Lights Engine Start Engine Turn Over Radio Lights Engine Start Engine Turn Over Radio Case I Case II

  8. 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 Start Engine Turn Over Radio Lights Engine Start Engine Turn Over Radio Case I Case II

  9. Battery Age Alternator Fan Belt Battery Age Alternator Fan Belt Leak Leak Charge Delivered Charge Delivered Battery Fuel Line Battery Fuel Line Starter Gas Distributor Starter Gas Distributor Battery Power Battery Power Spark Plugs Gas Gauge Spark Plugs Gas Gauge Lights Engine Start Engine Turn Over Radio Lights Engine Start Engine Turn Over Radio Decomposition Case I Case II

  10. 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

  11. A B B C A C D Decomposition Tree A B C D E B B E D

  12. 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

  13. 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)]

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

  15. Maximum Time: 560 sec Average Time: 38.6 sec

  16. Maximum Search Time: 1.8 sec Average Time: 1.3 sec

  17. 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

  18. Maximum Time: 430 sec

  19. 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

  20. 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

  21. Query Types • Pr: Posterior marginals • MPE: Most probable instantiation • MAP: Maximum a posteriori hypothesis

  22. Pr: Posterior Marginals Battery Age Alternator Fan Belt Charge Delivered Battery Fuel Pump Fuel Line Starter Distributor Gas Battery Power Spark Plugs Gas Gauge Engine Start Lights Engine Turn Over Radio

  23. 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 Engine Start Lights Engine Turn Over Radio

  24. 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 Engine Start Lights Engine Turn Over Radio

  25. 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 Engine Start Lights Engine Turn Over Radio

  26. 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 Engine Start Lights Engine Turn Over Radio

  27. 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 Engine Start Lights Engine Turn Over Radio

  28. 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

  29. 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.

  30. Scoring Neighbors using BP

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

  32. 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

  33. 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

  34. 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

  35. 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

  36. Deterministic Networks

  37. Big Networks • The third set is not amenable to exact solution so we compare relative solution quality

  38. 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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