Introduction
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Uncertainty: A state of having limited knowledge where it is
impossible to exactly describe the existing state, a future
outcome, or more than one possible outcome.
Ubiquitous in the world
Uncertainty and probability
Igor Farkaš
Centre for Cognitive Science
DAI FMFI Comenius University in Bratislava
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To deal with uncertainty, agents must keep track of belief states.
Probability is the measure of the likeliness that an event will occur
Alternative to logical approach
(Russell & Norvig: Artificial Intelligence, Prentice Hall, 2003)
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Probability basics
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Random variables
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Propositions
Using the probability
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Prior probability
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Conditional probability
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Bayes' rule
Independence
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Probability for continuous variables
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Interim summary
Alternative: Gaussian density
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Full Bayesian learning
Example
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Posterior probability of hypotheses
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Example of prediction probability
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MAP approximation
ML approximation
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Example: Linear Gaussian model
ML parameter learning in Bayes nets
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