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Machine Learning II DS 4420 - Spring 2020 MLE, MAP, & - PowerPoint PPT Presentation

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Machine Learning II DS 4420 - Spring 2020 MLE, MAP, & Graphical models Byron C. Wallace <latexit

  1. Machine Learning II DS 4420 - Spring 2020 MLE, MAP, & Graphical models Byron C. Wallace

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sha1_base64="lf+f7t3rAnWp0LosZvdc4nt/pT8=">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</latexit> Probability Spaces Definition: A probability space ( Ω , F, P) consists of • A sample space Ω (i.e. the set of outcomes ) • A set of events F (i.e. the set possible sets) • A probability measure P (maps events to probabilities) Axioms of Probability P : F → R

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