prml-slides-8 - PATTERN RECOGNITION AND MACHINE LEARNING...

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PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 8: GRAPHICAL MODELS
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Bayesian Networks Directed Acyclic Graph (DAG)
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Bayesian Networks General Factorization
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Bayesian Curve Fitting (1) Polynomial
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Bayesian Curve Fitting (2) Plate
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Bayesian Curve Fitting (3) Input variables and explicit hyperparameters
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Bayesian Curve Fitting Learning Condition on data
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Bayesian Curve Fitting Prediction Predictive distribution: where
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Generative Models Causal process for generating images
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Discrete Variables (1) General joint distribution: K 2 { 1 parameters Independent joint distribution: 2( K { 1) parameters
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Discrete Variables (2) General joint distribution over M variables: K M { 1 parameters M -node Markov chain: K { 1 + ( M { 1) K ( K { 1) parameters
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Discrete Variables: Bayesian Parameters (1)
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Discrete Variables: Bayesian Parameters (2) Shared prior
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Parameterized Conditional Distributions If are discrete, K -state variables, in general has O ( K M ) parameters. The parameterized form requires only M + 1 parameters
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Linear-Gaussian Models Directed Graph Vector-valued Gaussian Nodes Each node is Gaussian, the mean is a linear function of the parents.
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Conditional Independence a is independent of b given c Equivalently Notation
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Conditional Independence: Example 1
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Conditional Independence: Example 1
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Conditional Independence: Example 2
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prml-slides-8 - PATTERN RECOGNITION AND MACHINE LEARNING...

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