Expectation Maximization: a Gentle Introduction

This tutorial was basically written for students/researchers who want to get into first touch with the Expectation Maximization (EM) Algorithm. The main motivation for writing this tutorial was the fact that I did not find any text that fitted my needs. I started with the great book “Artificial Intelligence: A modern Approach”of Russel and Norvig [6], which provides lots of intuition, but I was disappointed that the general explication of the EM algorithm did not directly fit the shown examples. There is a very good tutorial written by Je↵ Bilmes [1]. However, I felt that some parts of the mathematical derivation could be shortened by another choice of the hidden variable (explained later on). Finally I had a look at the book “The EM Algorithm and Extensions” by McLachlan and Krishnan [4]. I can definitely recommend this book to anybody involved with the EM algorithm though, for a beginner, some steps could be more elaborate. So, I ended up by writing my own tutorial. Any feedback is greatly appreciated (error corrections, spelling/grammar mistakes, etc.).