Connecting ExpectationMaximization.jl to Optimizations.jl about expectationmaximization.jl

[dmetivie]

Hello,
Thanks for the interest. I knew just a bit about the Optimizations.jl. This sounds amazing.

I am not sure by what you exactly mean by “general enough” and what integration would look like.

The aim of this package is to implement EM algorithms (so far there is only the standard EM algo). In optimization terms:
— the function to optimize (maximize here) is the (log)-likelihood Lₓ(θ)
— where x are fixed parameters (the observed samples)
— θ are the optimization variable which corresponds to the Distributions (here MixtureDistribution) parameters.

Another way to see it is via the Distributions.jl package
I am just adding a new method for Distributions.fit_mle(D::T, x) when T is a MixtureDistribution.
For a few standard distributions like Normal and Exponential, the maximum found by fit_mle is explicitly known.
For other distributions, an optimization is needed, e.g. Gamma distribution. A lot of distributions do not have fit_mle implemented.
Would it also make sense to add the fit_mle function to the optimization package when actual numerical optimization is needed to find the maximum Likelihood estimator?