Expectation-maximization algorithm

Expectation-Maximization (EM) is a way of finding the best parameters of a model that represent some data. It's like trying to find the right pieces to make a puzzle.

Basically, you start with a bunch of pieces that could fit in the puzzle. You fit them together to see how they look and how they cover the image on the box. Then you start changing the pieces, trying different combinations and seeing how they look, until you get the best picture possible.

That's what EM does. It starts with some initial estimates of the parameters (pieces) and then it uses something called "expectation" to calculate how well the parameters match the data (how much the picture looks like the one on the box). Then it uses something called "maximization" to find the best combination of parameters that fit the data the best (the best picture possible).