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A Gentle Introduction to the EM Algorithm

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University of Minnesota, Duluth
University of Minnesota, Duluth

short presentation given at EMNLP 2001 during panel discussion

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A Gentle Introduction to the EM Algorithm Ted Pedersen Department of Computer Science University of Minnesota Duluth [email_address]
A unifying methodology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
A general framework for solving many kinds of problems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
EM allows us to make MLE under adverse circumstances ,[object Object],[object Object],[object Object],[object Object]
Maximum Likelihood Estimates ,[object Object],[object Object]
Coin Tossing! ,[object Object],[object Object],[object Object],[object Object],[object Object]
Coin tossing unmasked ,[object Object],[object Object]
Maximum Likelihood Estimates ,[object Object],[object Object]
Maximizing the likelihood
Multinomial MLE example ,[object Object],[object Object],[object Object],[object Object],[object Object]
Multinomial MLE example
Multinomial MLE example
Multinomial MLE runs aground? ,[object Object],[object Object],[object Object],[object Object],[object Object]
EM triumphs over adversity! ,[object Object],[object Object]
MLE for complete data
MLE for complete data
E-step ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
E-Step ,[object Object],[object Object],[object Object],[object Object],[object Object]
E-Step Iteration 1 ,[object Object],[object Object],[object Object]
M-Step iteration 1 ,[object Object]
E-Step Iteration 2 ,[object Object],[object Object],[object Object]
M-Step iteration 2 ,[object Object]
Result? ,[object Object],[object Object],[object Object]
Conclusion ,[object Object],[object Object],[object Object],[object Object],[object Object]

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