【一幅图解释EM算法】Parameter estimation for complete and incomplete data

(a) Maximum likelihood estimation. For each set of ten tosses, the maximum likelihood procedure accumulates the counts of heads and tails for coins A and B separately. These counts are then used to estimate the coin biases. 

(b) Expectation maximization.

1. EM starts with an initial guess of the parameters. 

2. In the E-step, a probability distribution over possible completions is computed using the current parameters. The counts shown in the table are the expected numbers of heads and tails according to this distribution. 

3. In the M-step, new parameters are determined using the current completions. 

4. After several repetitions of the E-step and M-step, the algorithm converges.