Download Quantifying Uncertainty

Quantifying
Uncertainty
Outline
qProbability theory - basics
qProbabilistic Inference
oInference by enumeration
qConditional Independence
qBayesian Networks
qInference in Bayesian Networks
oExact Inference
oApproximate Inference
qLearning Probabilistic Models
oNaïve Bayes Classifier
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
2
Non-monotonic logic
qTraditional logic is monotonic
oThe set of legal conclusions grows monotonically with
the set of facts appearing in our initial database
qWhen humans reason, we use defeasible logic
oAlmost every conclusion we draw is subject to reversal
oIf we find contradicting information later, we’ll want
to retract earlier inferences
qNonmonotonic logic, or defeasible reasoning,
allows a statement to be retracted
qSolution: Truth Maintenance
oKeep explicit information about which
facts/inferences support other inferences
oIf the foundation disappears, so must the conclusion
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
3
Uncertainty
qOn the other hand, the problem might not be
in the fact that T/F values can change over
time but rather that we are not certain of the
T/F value
qAgents almost never have access to the whole
truth about their environment
qAgents must act in the presence of
uncertainty
oIncompleteness and/or incorrectness of rules used by
the agent
oLimited and ambiguous sensors
oImperfection/noise in agent’s actions
oDynamic nature of the environment
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
4
Pitfalls of pure logic
qLaziness
oToo much work to list all conditions needed to
ensure an exceptionless rule
qTheoretical ignorance
oScience has no complete theory for the domain
qPractical ignorance
oEven if we know all the rules, we may be uncertain
about them
oWe only have a degree of belief in them
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
5
Probability Theory vs. Logic
qProbability - tool for handling degrees of
belief
oSummarizes uncertainty due to laziness and
ignorance
Logic
Ontological commitments
Epistemological commitments
world is composed of
facts that do or do not
hold
each sentence is true or false
or unknown
Probability world is composed of
Theory
facts that do or do not
hold
Quantifying Uncertainty
numerical degree of belief
between 0(sentence for
certainly false) and 1(sentences
are certainly true)
CSL452 - ARTIFICIAL INTELLIGENCE
6
Rational Agent Approach
qChoose action A that maximizes expected
utility
oMaximizes Prob(A)*Utility(A)
qProb(A) - probability that A will succeed
qUtility(A) - utility value to agent of A’s
outcomes
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
7
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
8
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
9
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
10
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
11
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
12
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
13
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
14
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
15
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
16
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
17
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
18
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
19
Quantifying Uncertainty
CSL452 - ARTIFICIAL INTELLIGENCE
20