lect14-15 Probability.pdf - www.monash.edu.au FIT5047 Intelligent Systems Probability Chapter 13 Some slides are adapted from Stuart Russell Andrew

lect14-15 Probability.pdf - www.monash.edu.au FIT5047...

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FIT5047: Intelligent Systems Probability Chapter 13 Some slides are adapted from Stuart Russell, Andrew Moore or Dan Klein
FIT5047 Intelligent Systems S1 2019 3 So far Agents did not consider: Uncertainty about the world or the outcome of an action Learning their knowledge

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FIT5047 Intelligent Systems S1 2019 4 From Now On Uncertainty Probability, Bayesian Networks Machine Learning Classification, Regression • Clustering
FIT5047 Intelligent Systems S1 2019 5 Outline Background: Random variables and probabilistic inference Probabilistic models Joint, marginal and conditional distributions Inference by enumeration Product Rule, Chain Rule, Bayes Rule Independence and conditional independence

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FIT5047 Intelligent Systems S1 2019 6 Reasoning under Uncertainty Uncertainty – the quality or state of being not clearly known – distinguishes deductive knowledge from inductive belief Sources of uncertainty – Ignorance – Complexity Physical randomness – Vagueness
FIT5047 Intelligent Systems S1 2019 7 Probability Calculus (I) Classic approach to reasoning under uncertainty (origin: Pascal and Fermat) Definitions: Experiment – produces one of several possible outcomes Sample space – the set of all possible outcomes Event – a subset of the sample space Random variable – a variable whose value is determined by the outcome of an experiment Probability function a function that assigns a probability to every possible outcome of an experiment Given a probability function we can define a probability for each value of a random variable

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FIT5047 Intelligent Systems S1 2019 8 Random Variables A random variable represents some aspect of the world about which we may have uncertainty R = Is it raining? D = How long will it take to drive to work? L = Where am I? We denote random variables with capital letters Random variables have domains R in {true, false} (sometimes write as {+r, r}) D in [0, ) L in possible locations, maybe {(0,0), (0,1), …}