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?


1 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
  • $\begingroup$ Thanks ,Could you please explain on what is meant by smoothly differentiable ? , i know that we have to find the best value for the mean vector ,covariance matrix using Expectation maximization $\endgroup$
    – star
    Jul 6, 2020 at 16:21

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