lecture 3 probability theory

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  

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  

Sta6s6cal  Methods…  

Natural  Language  Processing/Language  Technology  

The  No6on  of  Probability  

Sample  Spaces  

Events  

Composite  Experiments  

Axioms  of  Probability  

Simple  Probability:  Examples  

Theorems  of  Probability  

Condi6onal  Probability  

Example  1:  Dice  

Example  2:  Words  

Independence  

Independence:  Example  1  

Independence:  Example  2  

Independence  and  Incompa6bility  

The  end