On the Role of Channel Capacity in Learning Gaussian Mixture Models. (arXiv:2202.07707v2 [cs.IT] UPDATED)

This paper studies the sample complexity of learning the $k$ unknown centers
of a balanced Gaussian mixture model (GMM) in $\mathbb{R}^d$ with spherical
covariance matrix $\sigma^2\mathbf{I}$. In particular, we are interested in the
following question: what is the maximal noise level $\sigma^2$, for which the
sample complexity is essentially the same as when estimating the centers from
labeled measurements? To that end, we restrict attention to a Bayesian
formulation of the problem, where the centers are uniformly distributed on the …

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