概率图模型导论——概率论与图论相结合.ppt
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1、第十讲 概率图模型导论 Chapter 10 Introduction to Probabilistic Graphical Models,Weike Pan, and Congfu Xu panweike, Institute of Artificial Intelligence College of Computer Science, Zhejiang University October 12, 2006,浙江大学计算机学院人工智能引论课件,References,An Introduction to Probabilistic Graphical Models. Michael I.
2、Jordan. http:/www.cs.berkeley.edu/jordan/graphical.html,Outline,Preparations Probabilistic Graphical Models (PGM) Directed PGM Undirected PGM Insights of PGM,Outline,Preparations PGM “is” a universal model Different thoughts of machine learning Different training approaches Different data types Baye
3、sian Framework Chain rules of probability theory Conditional Independence Probabilistic Graphical Models (PGM) Directed PGM Undirected PGM Insights of PGM,Different thoughts of machine learning,Statistics (modeling uncertainty, detailed information) vs. Logics (modeling complexity, high level inform
4、ation) Unifying Logical and Statistical AI. Pedro Domingos, University of Washington. AAAI 2006. Speech: Statistical information (Acoustic model + Language model + Affect model) + High level information (Expert/Logics),Different training approaches,Maximum Likelihood Training: MAP (Maximum a Posteri
5、ori) vs. Discriminative Training: Maximum Margin (SVM) Speech: classical combination Maximum Likelihood + Discriminative Training,Different data types,Directed acyclic graph (Bayesian Networks, BN) Modeling asymmetric effects and dependencies: causal/temporal dependence (e.g. speech analysis, DNA se
6、quence analysis) Undirected graph (Markov Random Fields, MRF) Modeling symmetric effects and dependencies: spatial dependence (e.g. image analysis),PGM “is” a universal model,To model both temporal and spatial data, by unifying Thoughts: Statistics + Logics Approaches: Maximum Likelihood Training +
7、Discriminative Training Further more, the directed and undirected models together provide modeling power beyond that which could be provided by either alone.,Bayesian Framework,What we care is the conditional probability, and its is a ratio of two marginal probabilities.,A posteriori probability,Lik
8、elihood,Priori probability,Class i,Normalization factor,Observation,Problem description Observation Conclusion (classification or prediction),Bayesian rule,Chain rules of probability theory,Conditional Independence,Outline,Preparations Probabilistic Graphical Models (PGM) Directed PGM Undirected PGM
9、 Insights of PGM,PGM,Nodes represent random variables/states The missing arcs represent conditional independence assumptions The graph structure implies the decomposition,Directed PGM (BN),Representation,Conditional Independence,Probability Distribution,Queries,Implementation,Interpretation,Probabil
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- 概率 模型 导论 概率论 相结合
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