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1、Principle of Artificial IntelligencePart IIIUncertainty ReasoningContents1 Uncertainty, Probability and Reasoning (chpt13)2 Bayesian Networks and Reasoning (chpt14.114.4)3 Approximate Inference in BN (chpt14.5)4 Probabilistic Reasoning over Time (chpt15)Part 3 Uncertainty Reasoning3An example Tomorr
2、ow, outdoor activity (X ceremony, costly) Raining? Sunshine? Weather forecasts: sunshine=90%, rain=10% Cost=￥ 10,000: 10% chance to lose it = risk EOL (expected opportunity loss)=10% * cost = 1,000Part 3 Uncertainty Reasoning4Uncertainty & Risk (Wiki) Uncertainty: The lack of certainty, A state of h
3、aving limited knowledge where it is impossible to exactly describe existing state or future outcome, more than one possible outcome(多种可能性 ). Measurement of Uncertainty: A set of possible states or outcomes where probabilities are assigned to each possible state or outcome(概率 ). Risk: A state of unce
4、rtainty where some possible outcomes have an undesired effect or significant loss (不希望的可能 ). Measurement of Risk: A set of measured uncertainties where some possible outcomes are losses, and the magnitudes(量级 ) of those losses. Part 3 Uncertainty Reasoning5Uncertainty Pervasive in all of AI Search M
5、achine learning Computer vision Robotics Natural Language Processing Agents almost never have access to the whole truth about their environment.Part 3 Uncertainty Reasoning1Uncertainty, Probability and Reasoning (chpt. 13)1.1 Uncertainty and rational decisions1.2 Revisiting probability notations1.3
6、Reasoning with probabilityPart 3 Uncertainty Reasoning71.1 Uncertainty and rational decisions Requirements for uncertainty reasoning Summarizing uncertainty: probability Rational decisions for uncertaintyPart 3 Uncertainty Reasoning8Requirements for uncertainty reasoning (1) Incomplete information,
7、incomplete knowledge: asymmetrical (非对称 ) information, limited knowledge (on diseases) Confused and vague (模糊 ) information: descriptions from different people Noisy information (in data sets): natural, artificial Computational complexity for computing power (accurate reasoning unavailable) Flexible
8、 solutions (accurate reasoning unnecessary)Part 3 Uncertainty Reasoning9Requirements for UR (2) Fail with exact logic reasoning cavity (牙洞 ) toothache (one vs multiple, vice versa) Causes of reasoning failures Laziness: too much rules to be listed, cover each exception Theoretical ignorance: medical
9、 science has no complete theory for the domain Practical ignorance: general methods (even if a complete medical theory) vs. individuality (particular patient)Part 3 Uncertainty Reasoning10Summarizing uncertainty: probability Handling uncertainty: degree of belief in human mind quantifying ones belie
10、f probability theory Probability provide a way of summarizing (概括 ) the uncertainty that comes from our laziness and ignorance Statistical data: 80% toothache patients had cavities The coming-in toothache patient has an 80% chance with a cavityPart 3 Uncertainty Reasoning11Rational decisions for unc
11、ertainty (1) Multiple possible outcomes (some risks): our preference (偏好 ) between them Utility(效用 ) theory to represent and reason with preference Utility: a degree of usefulness to a state of an agent Different feeling for different people in the same utility degree (scores): examplePart 3 Uncerta
12、inty Reasoning12Rational decisions for uncertainty (2) Decision theory (reasoning) = probability theory + utility theory MEU (Maximum Expected Utility) principle: An agent is rational if and only if it chooses the action that yields the highest expected utility averaged over all the possible outcome
13、s of the action Averaged = statistical mean (均值 )Part 3 Uncertainty Reasoning131.2 Revisiting probability notations Possible world and its probability representation Probability axioms Bayes rule Independence & conditional independencePart 3 Uncertainty Reasoning14Possible world and its probability
14、representation All possible outcomes a value of the possible world: event (atomic event) the set of events: a proposition (命题 ) A possible world is defined to be an assignment of values to all of the random variables under consideration Weather=sunny, rain, cloudy, snow P(Weather)= (here bold: a vec
15、tor)Part 3 Uncertainty Reasoning15Full joint probability distributionweatherdrink sunny rainy cloudy snowdrink _today 0.13 0.11 0.15 0.08drink_today 0.31 0.04 0.15 0.03Part 3 Uncertainty Reasoning1)( P满足16Probability axioms (1) Probability axioms (Kolmogorovs axioms) We must yield it!Part 3 Uncertainty Reasoning1)(1)(0 Pande v e r yf o rP )()(, PPnp r o p o s i t i oanyf o r)()()|(bPbaPbaP )()()()( baPbPaPbaP )(1)( aPaP 17Probability axioms (2) Assume: P(a)=0.4 P(b)=0.3 P(ab)=0.0 P(ab)=0.8 If Agent 1 expresses a set of degrees of belief that violate the axioms of probability theory the
