# Bayesian Networks

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Bayesian Networks Recap of Last Lecture  Probability: Precise representation of uncertainty.  Probability Theory: Optimal updating of knowledge bared on new information.  Bayesian Inference  Conditional Probability ( | )  Product Rule (  Chain Rule ( ) ) ( | ) ( ) ( ) ( | ) ( | ∏ ( |  x, y independent iff ( ) ( ) ( ) ) ) ( ( ) )  x and y are conditionally independent of z iff ( | ) | ( | ) ( | ) Probabilistic Models  Models describe how (a portion of) the world works.  Models are al
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Bayesian Networks Recap of Last Lecture    Probability: Precise representation of uncertainty.    Probability Theory: Optimal updating of knowledge bared onnew information.    Bayesian Inference    Conditional Probability (|)()()      Product Rule ()(|)()      Chain Rule (        )(  )(  |  )(  |    )   ∏(  |        )       x, y independent iff  ()()()      x and y are conditionally independent of z iff  (|)(|)(|)     |    Probabilistic Models    Models describe how (a portion of) the world works.    Models are always simplifications    May not account for every variable    May not account for all interactions between variables    What do we do with probabilistic models?    We (or the agents) need to reason about the unknownvariables, given evidence.    Example:a)   Explanation (diagnostic reasoning)b)   Prediction (causal reasoning)c)   Value of information Probabilistic Reasoning    Suppose we go to my house and see that the door is open.    What’s the cause? Is it a burglar? Should we go in? Call the police?    Then again, it could be just be my wife. Maybe she camehome early.    How should we represent these relationships?  Bayes’ Nets: Big Picture      Two problems with using full joint distribution / tree tables asour probabilistic models. o   Unless there are only a few variables, the joint is way toobig to represent explicitly. For  variables with domainsize  joint tables has   entries. o   Hard to learn (estimate) anything empirically about morethan a few variables at a time.    Bayes’ nets: a technique for describing complex joint distributions (models) using simple local distributions(conditional probabilities) o   More properly called graphical models . o   We describe how variables locally interact. o   Local interactions chain together to give global indirectinteractions.  Graphical Model Notation    Causal relationships are represented in directed acyclic graphs.    Arrows (Arcs) indicates relationships between nodes.    For now: image that arrows mean direct causation (in global, they don’t)   Types of Probabilistic Relationships 1.   Independent ( |)()   (| )()  2.   Direct Cause (| )     opendoor wife burglar ABAB

Apr 14, 2018

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Apr 14, 2018
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