Graphic Model.pdf - Machine Learning 10-701 Tom M Mitchell...

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1 Machine Learning 10-701 Tom M. Mitchell Machine Learning Department Carnegie Mellon University October 11, 2011 Today: Graphical models Bayes Nets: Representing distributions Conditional independencies Simple inference Simple learning Readings: Required: Bishop chapter 8, through 8.2 Graphical Models Key Idea: – Conditional independence assumptions useful – but Naïve Bayes is extreme! – Graphical models express sets of conditional independence assumptions via graph structure – Graph structure plus associated parameters define joint probability distribution over set of variables Two types of graphical models: – Directed graphs (aka Bayesian Networks) – Undirected graphs (aka Markov Random Fields) today
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2 Graphical Models – Why Care? Among most important ML developments of the decade Graphical models allow combining: Prior knowledge in form of dependencies/independencies Prior knowledge in form of priors over parameters Observed training data Principled and ~general methods for Probabilistic inference – Learning Useful in practice Diagnosis, help systems, text analysis, time series models, ... Conditional Independence Definition : X is conditionally independent of Y given Z, if the probability distribution governing X is independent of the value of Y, given the value of Z Which we often write E.g.,
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3 Marginal Independence Definition : X is marginally independent of Y if Equivalently, if Equivalently, if Represent Joint Probability Distribution over Variables
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4 Describe network of dependencies Bayes Nets define Joint Probability Distribution in terms of this graph, plus parameters Benefits of Bayes Nets: Represent the full joint distribution in fewer parameters, using prior knowledge about dependencies Algorithms for inference and learning
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5 Bayesian Networks Definition A Bayes network represents the joint probability distribution over a collection of random variables A Bayes network is a directed acyclic graph and a set of conditional probability distributions (CPD’s)
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  • Fall '11
  • Mitchell,Tom
  • Probability theory, Bayesian network

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