Expectation Maximization Algorithm. Rong Jin. A Mixture Model Problem. Apparently, the dataset consists of two modes How can we automatically identify the two modes?. Gaussian Mixture Model (GMM). Assume that the dataset is generated by two mixed Gaussian distributions Gaussian model 1:
We are luck here. In general, this step can be extremely difficult and usually requires approximate approaches
Can we use the concave property of logarithm function?
No, we can’t because we need a lower bound
Wait a minute, this can not be right! What happens?
Where does it go wrong?
Is this solution unique?
Try out the standard numerical methods before you get excited about your algorithm
Limited-memory Quasi-Newton method
Improved iterative scaling