Why Gaussian mixture model uses Expectation maximization instead of Gradient descent?

Question

Why Gaussian mixture model uses Expectation maximization instead of Gradient descent?

What other models uses Expectation maximization to find best optimal parameters instead of using gradient descent?

Answer 1

Not all the parameters (e.g., the assignment parameters) for a Gaussian mixture model are smoothly differentiable, thus can not be fit with gradient descent.

Other use cases for the expectation–maximization (EM) algorithm are:

• Clustering
• Latent variable estimation
• Missing data estimation