383-Fall11-Lec13

# 383-Fall11-Lec13 - Dealing with Uncertainty CMPSCI 383 1...

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1 CMPSCI 383 October 25, 2011 Dealing with Uncertainty

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2 Midterm grades 0 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Series1 Average: 71
3 Outline Uncertainty Probability Syntax and Semantics Inference Independence and Bayes' Rule

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4 Uncertainty Let action A t = leave for airport t minutes before Fight Will A t get me there on time? Problems • Partial observability (road state, other drivers' plans, etc.) • Noisy sensors (trafFc reports) • Uncertainty in action outcomes (±at tire, etc.) • Immense complexity of modeling and predicting trafFc A purely logical approach either. .. • Risks falsehood: “ A 25 will get me there on time”, or • Leads to conclusions that are too weak for decision making A 25 will get me there on time if there's no accident on the bridge and it doesn't rain and my tires remain intact etc etc.” (qualiFcation problem) A 1440 might reasonably be said to get me there on time but I'd have to stay overnight in the airport …”
5 Options for handling uncertainty Belief states and contingency plans Default or nonmonotonic logic Assume my car does not have a Fat tire Assume A 25 works unless contradicted by evidence However. .. What assumptions are reasonable? How to handle contradiction? Rules with fudge factors A 25 | 0.3 get there on time Sprinkler | 0.99 WetGrass WetGrass | 0.7 Rain However. .. Problems with combination, e.g., Sprinkler causes Rain ?? Probability Model agent's degree of belief Given the available evidence, A 25 will get me there on time with probability 0.04

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6 Probability Probabilistic assertions summarize effects of Laziness — failure to enumerate exceptions, qualiFcations, etc. Ignorance —lack of relevant facts, initial conditions, etc. ±undamental stochastic nature of phenomena Subjective probability Probabilities relate propositions to agent's own state of knowledge e.g., P(A 25 | no reported accidents) = 0.06 These are not assertions about the world, they are assertions about belief Probabilities of propositions change with new evidence: e.g., P(A 25 | no reported accidents, 5 a.m.) = 0.15
7 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 | …)

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383-Fall11-Lec13 - Dealing with Uncertainty CMPSCI 383 1...

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