lecture22.pdf

# lecture22.pdf - COMPSCI 240 Reasoning Under Uncertainty...

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COMPSCI 240: Reasoning Under Uncertainty Arya Mazumdar University of Massachusetts at Amherst Fall 2016

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Lecture 22
Bayesian Network

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Bayesian Networks A Bayesian network uses conditional independence assumptions to more compactly represent a joint PMF of many random variables.
Bayesian Networks A Bayesian network uses conditional independence assumptions to more compactly represent a joint PMF of many random variables. We use a directed acyclic graph to encode conditional independence assumptions.

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Bayesian Networks A Bayesian network uses conditional independence assumptions to more compactly represent a joint PMF of many random variables. We use a directed acyclic graph to encode conditional independence assumptions. I Nodes X i in the graph G represent random variables.
Bayesian Networks A Bayesian network uses conditional independence assumptions to more compactly represent a joint PMF of many random variables. We use a directed acyclic graph to encode conditional independence assumptions. I Nodes X i in the graph G represent random variables. I A directed edge X j X i means X j is a “parent” of X i .

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Bayesian Networks A Bayesian network uses conditional independence assumptions to more compactly represent a joint PMF of many random variables. We use a directed acyclic graph to encode conditional independence assumptions. I Nodes X i in the graph G represent random variables. I A directed edge X j X i means X j is a “parent” of X i . I This means X i directly depends on X j
Bayesian Networks A Bayesian network uses conditional independence assumptions to more compactly represent a joint PMF of many random variables. We use a directed acyclic graph to encode conditional independence assumptions. I Nodes X i in the graph G represent random variables. I A directed edge X j X i means X j is a “parent” of X i . I This means X i directly depends on X j I The set of variables that are parents of X i is denoted Pa i .

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Bayesian Networks A Bayesian network uses conditional independence assumptions to more compactly represent a joint PMF of many random variables. We use a directed acyclic graph to encode conditional independence assumptions. I Nodes X i in the graph G represent random variables. I A directed edge X j X i means X j is a “parent” of X i . I This means X i directly depends on X j I The set of variables that are parents of X i is denoted Pa i . I Each variable is conditionally independent of all its nondescendants in the graph given the value of all its parents.
Bayesian Networks A Bayesian network uses conditional independence assumptions to more compactly represent a joint PMF of many random variables.

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