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Representation and Reasoning with Graphical Models

Representation and Reasoning with Graphical Models. Rina Dechter Information and Computer Science, UC-Irvine, and Radcliffe Institue of Advanced Study, Cambridge. Outline. Introduction to reasoning in AI Graphical models Constraint networks Probabilistic networks Graph-based reasoning.

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Representation and Reasoning with Graphical Models

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  1. Representation and Reasoning with Graphical Models Rina Dechter Information and Computer Science, UC-Irvine, and Radcliffe Institue of Advanced Study, Cambridge

  2. Outline • Introduction to reasoning in AI • Graphical models • Constraint networks • Probabilistic networks • Graph-based reasoning Radcliffe Institute 2/6/06

  3. The Turing Test(Can Machine think? A. M. Turing, 1950) • Requires • Natural language • Knowledge representation • Automated reasoning • Machine learning • (vision, robotics) for full test Radcliffe Institute 2/6/06

  4. = A = B = A = C Propositional Reasoning Example: party problem • If Alex goes, then Becky goes: • If Chris goes, then Alex goes: • Question: Is it possible that Chris goes to the party but Becky does not? Radcliffe Institute 2/6/06

  5. Sudoku –Constraint Satisfaction • Variables: empty slots • Domains = {1,2,3,4,5,6,7,8,9} • Constraints: • 27 all-different • Constraint • Propagation • Inference 2 34 6 2 Each row, column and major block must be alldifferent “Well posed” if it has unique solution: 27 constraints Radcliffe Institute 2/6/06

  6. A B A B C B C A D C E D E G H D E F F G L K J F G H J M Directed graph A graph A tree E B A M F J N C K G D O L H P A graph with one cycle Graphs Radcliffe Institute 2/6/06

  7. E A B red green red yellow green red green yellow yellow green yellow red A D B F G C Constraint Networks A Example: map coloring Variables - countries (A,B,C,etc.) Values - colors (red, green, blue) Constraints: Constraint graph A E D F B G C Radcliffe Institute 2/6/06

  8. Constraint Satisfaction Tasks Example: map coloring Variables - countries (A,B,C,etc.) Values - colors (e.g., red, green, yellow) Constraints: Are the constraints consistent? Find a solution, find all solutions Count all solutions Find a good solution Radcliffe Institute 2/6/06

  9. Information as Constraints • I have to finish my talk in 30 minutes • 180 degrees in a triangle • Memory in our computer is limited • The four nucleotides that makes up a DNA only combine in a particular sequence • Sentences in English must obey the rules of syntax • Susan cannot be married to both John and Bill • Alexander the Great died in 333 B.C. Radcliffe Institute 2/6/06

  10. Applications • Planning and scheduling • Transportation scheduling, factory scheduling • Configuration and design problems • floorplans • Circuit diagnosis • Scene labeling • Spreadsheets • Temporal reasoning, Timetabling • Natural language processing • Puzzles: crosswords, sudoku, cryptarithmetic Radcliffe Institute 2/6/06

  11. P(A|W=bad)=.9 W A P(C|W=bad)=.1 W C W B P(B|W=bad)=.5 P(W) W A B C P(A|W) P(B|W) P(C|W) Probabilistic Reasoning Party example: the weather effect • Alex is-likely-to-go in bad weather • Chris rarely-goes in bad weather • Becky is indifferent but unpredictable Questions: • Given bad weather, which group of individuals is most likely to show up at the party? • What is the probability that Chris goes to the party but Becky does not? P(W,A,C,B) = P(B|W) · P(C|W) · P(A|W) · P(W) P(A,C,B|W=bad) = 0.9 · 0.1 · 0.5 Radcliffe Institute 2/6/06

  12. P(S) P(C|S) P(B|S) • C B P(D|C,B) • 0 0 0.1 0.9 • 0 1 0.7 0.3 • 1 0 0.8 0.2 • 1 1 0.9 0.1 CPD: P(X|C,S) P(D|C,B) Bayesian Networks: Representation(Pearl, 1988) Smoking lung Cancer Bronchitis X-ray Dyspnoea P(S, C, B, X, D)= P(S) P(C|S) P(B|S) P(X|C,S) P(D|C,B) Belief Updating: P (lung cancer=yes | smoking=no, dyspnoea=yes ) = ? Radcliffe Institute 2/6/06

  13. MINVOLSET KINKEDTUBE PULMEMBOLUS INTUBATION VENTMACH DISCONNECT PAP SHUNT VENTLUNG VENITUBE PRESS MINOVL FIO2 VENTALV PVSAT ANAPHYLAXIS ARTCO2 EXPCO2 SAO2 TPR INSUFFANESTH HYPOVOLEMIA LVFAILURE CATECHOL LVEDVOLUME STROEVOLUME ERRCAUTER HR ERRBLOWOUTPUT HISTORY CO CVP PCWP HREKG HRSAT HRBP BP Monitoring Intensive-Care Patients The “alarm” network - 37 variables, 509 parameters (instead of 237) Radcliffe Institute 2/6/06

  14. Sample Domains • Web Pages and Link Analysis • Battlespace Awareness • Epidemiological Studies • Citation Networks • Communication Networks (Cell phone Fraud Detection) • Intelligence Analysis (Terrorist Networks) • Financial Transactions (Money Laundering) • Computational Biology • Object Recognition and Scene Analysis • Natural Language Processing (e.g. Information Extraction and Semantic Parsing) Radcliffe Institute 2/6/06

  15. Graphical models in News:The New York Times, Dec 15, 2005 • Three Technology Companies Join to Finance Research in Graphical Models • David Patterson, center, founding director of the Berkeley lab, talks with Prof. Michael Jordan of Berkeley, right, and Prof. Armando Fox of Stanford. Radcliffe Institute 2/6/06

  16. Complexity of Reasoning Tasks • Constraint satisfaction • Counting solutions • Combinatorial optimization • Belief updating • Most probable explanation • Decision-theoretic planning Reasoning is computationally hard Complexity is Time and space(memory) Radcliffe Institute 2/6/06

  17. P(X) P(Y|X) P(Z|X) P(T|Y) P(R|Y) P(L|Z) P(M|Z) Tree-solving is easy CSP – consistency (projection-join) Belief updating (sum-prod) #CSP (sum-prod) MPE (max-prod) Trees are processed in linear time and memory Radcliffe Institute 2/6/06

  18. Transforming into a Tree • By Inference (thinking) • Transform into a single, equivalent tree of sub-problems • By Conditioning (guessing) • Transform into many tree-like sub-problems. Radcliffe Institute 2/6/06

  19. Inference and Treewidth ABC DGF G D A B BDEF F C EFH E M K H FHK L J Inference algorithm: Time: exp(tree-width) Space: exp(tree-width) HJ KLM treewidth = 4 - 1 = 3 treewidth = (maximum cluster size) - 1 Radcliffe Institute 2/6/06

  20. H H H G G G N N N H H G G D D D N N F F F M M M D D A A A A J J J F F M M O O O J J E E E O O E E C C C P P P B B B C C P P B B K K K L L L K K L L B H H H G G G N N N D D D C F F M M F M J J J O O O E E E C C P P P K K L L K L Conditioning and Cycle cutset Cycle cutset = {A,B,C} Radcliffe Institute 2/6/06

  21. E M D Graph Coloring problem L C A B K H F G J A=yellow A=green E M E M D D L L C C B B K K H H F F G G J J Search over the Cutset • Inference may require too much memory • Condition (guessing) on some of the variables Radcliffe Institute 2/6/06

  22. E M D Graph Coloring problem L C A B K H F G J A=yellow A=green B=red B=blue B=green B=red B=blue B=yellow E E E E E E M M M M M M D D D D D D L L L L L L C C C C C C K K K K K K H H H H H H F F F F F F G G G G G G J J J J J J Search over the Cutset (cont) • Inference may require too much memory • Condition on some of the variables Radcliffe Institute 2/6/06

  23. ABC DGF G D A BDEF B F C EFH E M K H FHK L J KLM HJ A=yellow A=green B=blue B=green B=red B=blue E M D L C A E E E E M M M M D D D D L L L L B K C C C C H F K K K K G J H H H H F F F F G G G G J J J J Inference vs. Conditioning • By Inference (thinking) Exponential in treewidth Time and memory • By Conditioning (guessing) Exponential in cycle-cutset Time-wise, linear memory Radcliffe Institute 2/6/06

  24. My Work • Constraint networks: Graph-based parameters and algorithms for constraint satisfaction, tree-width and cycle-cutset, summarized in “Constraint Processing”, Morgan Kaufmann, 2003 • Probabilistic networks: Transferring these ideas to Probabilistic network, helping unifying the principles. • Current work: Mixing probabilistic and deterministic network Radcliffe Institute 2/6/06

  25. B A F C S D B A F C S D Research in Radcliffe:Mixed Probabilistic and Deterministic networks B A BN 1. CN F C 2. D E 3. Mix: combine? Subsume? B A Semantic? Algorithms? F C Radcliffe Institute 2/6/06 D E

  26. P(W) P(W) B B A A C C W W A→B A→B C→A C→A P(B|W) P(B|W) P(C|W) P(C|W) P(A|W) P(A|W) B B A A C C Research in Radcliffe:Mixed Probabilistic and Deterministic networks PN CN Query: Is it likely that Chris goes to the party if Becky does not but the weather is bad? Semantics? Algorithms? Radcliffe Institute 2/6/06

  27. The End Thank You

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