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Machine Learning for Language Technology Lecture 4: Sta,s,cal Inference Marina San,ni Department of Linguis,cs and Philology Uppsala University, Uppsala, Sweden Autumn 2014 Acknowledgement: Thanks to Prof. Joakim Nivre for course design and materials
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Lecture 4: Statistical Inference

Dec 05, 2014

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Marina Santini

Basic concepts of statistical inference.
Outline:
stochastic variables, frequency functions, expectations, variance, entropy, joint probabilities, conditional probabilities, independence, sampling, estimation, maximum likelihood estimation (MLE), smoothing, hypothesis testing,z-test,
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Page 1: Lecture 4: Statistical Inference

Machine  Learning  for  Language  Technology    Lecture  4:  Sta,s,cal  Inference  

Marina  San,ni  Department  of  Linguis,cs  and  Philology  Uppsala  University,  Uppsala,  Sweden  

 Autumn  2014  

 Acknowledgement:  Thanks  to  Prof.  Joakim  Nivre  for  course  design  and  materials  

Page 2: Lecture 4: Statistical Inference

Stochas,c  Variables  

Page 3: Lecture 4: Statistical Inference

Types  of  Variables  

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Frequency  Func,ons  

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Expecta,on  

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Variance  

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Entropy  

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More  on  Entropy  

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Joint  and  Condi,onal  Probability  

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Independence  

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Part-­‐of-­‐Speech  Bigrams  1  

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Part-­‐of-­‐Speech  Bigrams  2  

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Part-­‐of-­‐Speech  Bigrams  3  

Page 14: Lecture 4: Statistical Inference

Sta,s,cal  Inference  

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Sampling  

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Es,ma,on  

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Maximum  Likelihood  Es,ma,on  (MLE)  

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MLE:  Example  1  

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MLE:  Example  2  

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MLE:  Ra,onale  

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MLE  and  Smoothing  

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Interval  Es,ma,on  

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More  on  Interval  Es,ma,on  

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Hypothesis  Tes,ng  

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Example:  Z-­‐test  

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The  end