What is an intuitive explanation of the Expectation Maximization technique?

The accepted answer references the Chuong EM Paper, which does a decent job explaining EM. There is also a youtube video that explains the paper in more detail.

To recap, here is the scenario:

1st:  {H,T,T,T,H,H,T,H,T,H} 5 Heads, 5 Tails; Did coin A or B generate me?
2nd:  {H,H,H,H,T,H,H,H,H,H} 9 Heads, 1 Tails
3rd:  {H,T,H,H,H,H,H,T,H,H} 8 Heads, 2 Tails
4th:  {H,T,H,T,T,T,H,H,T,T} 4 Heads, 6 Tails
5th:  {T,H,H,H,T,H,H,H,T,H} 7 Heads, 3 Tails

Two possible coins, A & B are used to generate these distributions.
A & B have an unknown parameter: their bias towards heads.

We don't know the biases, but we can simply start with a guess: A=60% heads, B=50% heads.

In the case of the first trial's question, intuitively we'd think B generated it since the proportion of heads matches B's bias very well... but that value was just a guess, so we can't be sure.

With that in mind, I like to think of the EM solution like this:

• Each trial of flips gets to 'vote' on which coin it likes the most
  • This is based on how well each coin fits its distribution
  • OR, from the point of view of the coin, there is high expectation of seeing this trial relative to the other coin (based on log likelihoods).
• Depending on how much each trial likes each coin, it can update the guess of that coin's parameter (bias).
  • The more a trial likes a coin, the more it gets to update the coin's bias to reflect its own!
  • Essentially the coin's biases are updated by combining these weighted updates across all trials, a process called (maximazation), which refers to trying to get the best guesses for each coin's bias given a set of trials.

This may be an oversimplification (or even fundamentally wrong on some levels), but I hope this helps on an intuitive level!