Computational Information Geometry Wonderland

When learning statistical mixtures, there are two basic questions: (1) how good can we learn a model, and (2) how fast can we do it?
At ICASSP, we have presented k-MLE for learning mixtures with k components by maximizing the complete likelihood function.
Another strategy, is to start from a kernel density estimator, and then simplify it. For 1D normal mixtures, the Fisher-Rao geometry amounts to hyperbolic geometry, but the centroid has not a closed-form. We have proposed to use another definition of center of mass in closed form in hyperbolic geometry to simplify a KDE. Thus we learn a mixture by simplifying a KDE.
The details of the paper are here.
Frank.