Lecture 3 Probability Theory

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Statistical methods and Natural Language Processing/Language Technology

Notion of Probability
Sample Spaces
Events
Axioms of Probability
Theorems of Probability
Conditional Probability
Independence and Incompatibility

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Lecture 3 Probability Theory

  1. 1. Machine  Learning  for  Language  Technology     Lecture  3:  Probability  Theory   Marina  San6ni   Department  of  Linguis6cs  and  Philology   Uppsala  University,  Uppsala,  Sweden     Autumn  2014     Acknowledgement:  Thanks  to  Prof.  Joakim  Nivre  for  course  design  and  materials  
  2. 2. Outline   •  Sta6s6cal  methods  and  Natural  Language  Processing/ Language  Technology   •  No6on  of  Probability   •  Sample  Spaces   •  Events   •  Axioms  of  Probability   •  Theorems  of  Probability   •  Condi6onal  Probability   •  Independence  and  Incompa6bility  
  3. 3. Sta6s6cal  Methods…  
  4. 4. Natural  Language  Processing/Language  Technology  
  5. 5. The  No6on  of  Probability  
  6. 6. Sample  Spaces  
  7. 7. Events  
  8. 8. Composite  Experiments  
  9. 9. Axioms  of  Probability  
  10. 10. Simple  Probability:  Examples  
  11. 11. Theorems  of  Probability  
  12. 12. Condi6onal  Probability  
  13. 13. Example  1:  Dice  
  14. 14. Example  2:  Words  
  15. 15. Independence  
  16. 16. Independence:  Example  1  
  17. 17. Independence:  Example  2  
  18. 18. Independence  and  Incompa6bility  
  19. 19. The  end  
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