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Unformatted text preview: Uncertainty Chapter 13 Chapter 13 1 Outline Uncertainty Probability Syntax and Semantics Inference Independence and Bayes Rule Chapter 13 2 Uncertainty Let action A t = leave for airport t minutes before flight Will A t get me there on time? Problems: 1) partial observability (road state, other drivers plans, etc.) 2) noisy sensors (KCBS tra ffi c reports) 3) uncertainty in action outcomes (flat tire, etc.) 4) immense complexity of modelling and predicting tra ffi c Hence a purely logical approach either 1) risks falsehood: A 25 will get me there on time or 2) leads to conclusions that are too weak for decision making: A 25 will get me there on time if theres no accident on the bridge and it doesnt rain and my tires remain intact etc etc. ( A 1440 might reasonably be said to get me there on time but Id have to stay overnight in the airport ... ) Chapter 13 3 Methods for handling uncertainty Default or nonmonotonic logic: Assume my car does not have a flat tire Assume A 25 works unless contradicted by evidence Issues: What assumptions are reasonable? How to handle contradiction? Rules with fudge factors : A 25 . 3 AtAirportOnTime Sprinkler . 99 WetGrass WetGrass . 7 Rain Issues: Problems with combination, e.g., Sprinkler causes Rain ?? Probability Given the available evidence, A 25 will get me there on time with probability . 04 Mahaviracarya (9th C.), Cardamo (1565) theory of gambling ( Fuzzy logic handles degree of truth NOT uncertainty e.g., WetGrass is true to degree . 2 ) Chapter 13 4 Probability Probabilistic assertions summarize e ff ects of laziness : failure to enumerate exceptions, qualifications, etc. ignorance : lack of relevant facts, initial conditions, etc. Subjective or Bayesian probability: Probabilities relate propositions to ones own state of knowledge e.g., P ( A 25  no reported accidents ) = 0 . 06 These are not claims of a probabilistic tendency in the current situation (but might be learned from past experience of similar situations) Probabilities of propositions change with new evidence: e.g., P ( A 25  no reported accidents , 5 a.m. ) = 0 . 15 (Analogous to logical entailment status KB  = , not truth.) Chapter 13 5 Making decisions under uncertainty Suppose I believe the following: P ( A 25 gets me there on time  ... ) = 0 . 04 P ( A 90 gets me there on time  ... ) = 0 . 70 P ( A 120 gets me there on time  ... ) = 0 . 95 P ( A 1440 gets me there on time  ... ) = 0 . 9999 Which action to choose? Depends on my preferences for missing flight vs. airport cuisine, etc. Utility theory is used to represent and infer preferences Decision theory = utility theory + probability theory Chapter 13 6 Probability basics Begin with a set the sample space e.g., 6 possible rolls of a die....
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This note was uploaded on 02/07/2012 for the course CSCI 5512 taught by Professor Staff during the Spring '08 term at Minnesota.
 Spring '08
 Staff

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