# Expectation Maximization (EM Algorithm) for Missing Data

I'm having trouble understanding Expectation Maximization specifically in the context of using it fill in missing data. I understand the general principle outlined in previous posts, but I do not see how this is implemented step-wise for missing data.

As an example, if I have sets of repeated data in the format of (a,b,c,d) but I'm missing a single value in one of the series, what are the first pass "E" and "M" steps that lead to predicting the missing value? I assume EM leverages the completed data examples to predict the missing value, but I'm unsure of the steps.

Example 1 - (0,1,1,1)

Example 2 - (1,1,0,0)

Example 3 - (1,0,0,0)

Example 4 - (1,0,1,1)

Example 5 - (1,?,0,1) Missing Data

• This is not the type of example where the EM algorithm shines. I suggest to have a look into the book of Pachter and Sturmfels about algebraic statistics for computational biology. – Wuestenfux Nov 3 '17 at 19:09
• I'm somewhat aware that this might not be its "ideal" test case. However, I'm trying to understand if EM can be used to fill in data like this. Often machine learning examples are formatted this way and include missing data. As an example, imagine these examples are True/false user preferences and I'm training an algorithm to predict a future user's preferences. It would be advantageous to use EM to predict the missing values if one user left off a preference. – E. Camus Nov 3 '17 at 22:08