Unformatted text preview:

Uncertain ReasoningReasoning in Complex Domains or SituationsForms of Uncertain ReasoningMaking Decisions to Meet GoalsQuick QuestionQuick Question 2Basics of ProbabilitySlide 8Slide 9Bayes’ RuleReasoning with Bayes’ RuleSlide 12Slide 13Slide 14Combining EvidenceIndependence of EventsConditional IndependenceSlide 18Human ReasoningSlide 20Uncertain Reasoning CPSC 315 – Programming StudioSpring 2009Project 2, Lecture 6Reasoning in Complex Domains or SituationsReasoning often involves moving from evidence about the world to decisionsSystems almost never have access to the whole truth about their environmentReasons for lack of knowledgeCost/benefit trade-off in knowledge engineeringLess likely, less influential factors often not included in modelNo complete theory of domainComplete theories are few and far betweenIncomplete knowledge of situationAcquiring all knowledge of situation is impracticalForms of Uncertain ReasoningPartially-believed domain featuresE.g. chance of rain = 80%Probability (focus of today’s lecture)Other (we will return to this)Partially-true domain featuresE.g. cloudy = .8Fuzzy logic (outside scope of this class)Making Decisions to Meet GoalsDecision theory = Probability theory +Utility theoryDecisions – the outcome of system’s reasoning, actions to take or avoidProbability – how system reasonsUtility – system’s goals / preferencesQuick QuestionYou go to the doctor and are tested for a disease. The test is 98% accurate if you have the disease. 3.6% of the population has the disease while 4% of the population tests positive.How likely is it you have the disease?Quick Question 2You go to the doctor and are tested for a disease. The test is 98% accurate if you have the disease. 3.6% of the population has the disease while 7% of the population tests positive.How likely is it you have the disease?Basics of ProbabilityUnconditional or prior probabilityDegree of belief of something being true in absence of any informationP (cavity = true) = 0.1 or P (cavity) = 0.1Implies P (not cavity) = 0.9Basics of ProbabilityUnconditional or prior probabilityCan be for a set of valuesP (Weather = sunny) = 0.7P (Weather = rain) = 0.2P (Weather = cloudy) = .08P (Weather = snow) = .02Note: Weather can have only a single value – system must know that rain and snow implies cloudsBasics of ProbabilityConditional or posterior probabilityDegree of belief of something being true given knowledge about situationP (cavity | toothache) = 0.8Mathematically, we knowP (a | b) = P (a ^ b) / P (b)Requires system to know unconditional probability of combinations of featuresThis knowledge becomes exponential relative to the size of the feature setBayes’ RuleRemember: P (a | b) = P (a ^ b) / P (b)Can be rewrittenP (a ^ b) = P (a | b) * P (b)Swapping a and b features yieldsP (a ^ b) = P (b | a) * P (a)ThusP (b | a) * P (a) = P (a | b) * P (b) Rewriting we get Bayes’ RuleP (b | a) = P (a | b) * P (b) / P (a)Reasoning with Bayes’ RuleBayes’ RuleP (b | a) = P (a | b) * P (b) / P (a)ExampleLet’s take P (disease) = 0.036P (test) = 0.04P (test | disease) = 0.98P (disease | test) = ?Reasoning with Bayes’ RuleBayes’ RuleP (b | a) = P (a | b) * P (b) / P (a)ExampleP (disease) = 0.036P (test) = 0.04P (test | disease) = 0.98P (disease | test) = ? = P (test | disease) * P (disease) / P (test) = 0.98 * 0.036 / 0.04 = 88.2 %Reasoning with Bayes’ RuleWhat if test has more false positivesStill 98% accurate for those with diseaseExampleP (disease) = 0.036P (test) = 0.07P (test | disease) = 0.98P (disease | test) = ? = P (test | disease) * P (disease) / P (test) = 0.98 * 0.036 / 0.07 = 50.4 %Reasoning with Bayes’ RuleWhat if test has more false negativesNow 90% accurate for those with diseaseExampleP (disease) = 0.036P (test) = 0.04P (test | disease) = 0.90P (disease | test) = ? = P (test | disease) * P (disease) / P (test) = 0.90 * 0.036 / 0.04 = 81 %Combining EvidenceWhat happens when we have more than one piece of evidenceExample: toothache and tool catches on toothP (cavity | toothache ^ catch) = ?Problem: toothache and catch are not independentIf someone has a toothache there is a greater chance they will have a catch and vice-versaIndependence of EventsIndependence of features / eventsFeatures / events cannot be used to predict each otherExample: values rolled on two separate dieExample: hair color and food preferenceProbabilistic reasoning works because systems divide domain into independent sub-domainsDo not need the exponentially increasing data to understand interactionsUnfortunately, non-independent sub-domains can still be huge (have many interacting features)Conditional IndependenceWhat happens when we have more than one piece of evidenceExample: toothache and tool catches on toothP (cavity | toothache ^ catch) = ?Conditional independenceAssume indirect relationshipExample: toothache and catch are both caused by cavity but not any other featureThen P (toothache ^ catch | cavity) = P (toothache | cavity) * P (catch | cavity)Conditional IndependenceThis let’s us sayP (toothache ^ catch | cavity)= P (toothache | cavity) * P (catch | cavity)P (cavity | toothache ^ catch) = ?= P (toothache ^ catch | cavity) * P (cavity)= P (toothache | cavity) * P (catch | cavity) * P (cavity)Avoids requiring system to have data on all permutationsDifficulty: How true?What about a chipped or cracked tooth?Human ReasoningStudies show people, without training and prompting, do not reason probabilisticallyPeople make incorrect inferences when confronted with probabilities like those of the last few slidesIf asked for all prior and posterior probabilities then they will posit systems with rather large inconsistenciesHuman ReasoningStudies show people, without training, do not reason probabilisticallySome systems have used non-probabilistic forms of uncertain reasoningQualitative categories rather than numbers Must be true, highly likely, likely, some chance, unlikely, virtually impossible, impossibleRules for how these combine based on human


View Full Document

TAMU CSCE 315 - AIUncertainty

Download AIUncertainty
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view AIUncertainty and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view AIUncertainty 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?