What results exist for computing (or approximating) the entropy of a mixture of von Mises-Fisher distributions?
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$\begingroup$ Is the entropy known for a single vMF distribution? ("trivial mixture") I don't know about entropy approximations for general mixtures, but maybe one could combine two such procedures. E.g. arxiv.org/abs/2202.05192 If one could use f-divergence to estimate KL divergence, and that to estimate entropy for a single vMF distribution, then maybe one could get somewhere. It sounds difficult though $\endgroup$– hasManyStupidQuestionsCommented May 13, 2023 at 18:29
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I'm not an expert on statistics but from my understanding of 10.1109/ISBI.2006.1624853 it seems the Shannon entropy of a vMF mixture could not be written in closed form. Certain Rényi entropies (e.g. quadratic) can, though (see Section 2.2).
