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Hi, Is there any proved result concerning the universal approximation ability of a mixture of Gaussians? if so, could you provide a reference? Thanks. |
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I have been told and have found on wikipedia (with no further source), that centroid based clustering (GMMs are centroid based) is NP-hard. This applies when you do not have labels but you do know the number of clusters. |
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Assuming I'm interpreting your question correctly, a Google search reveals that this question also appears on Math Overflow with a few answers: http://mathoverflow.net/questions/27589/mixtures-of-gaussian-distributions-dense-in-distributions Thanks, I wasn't aware of this question. They seem to be similar, but on MO it is about approximating a probability distribution, while universal approximation talks about approximating continuous real functions by neural networks, as in http://en.wikipedia.org/wiki/Universal_approximation_theorem.
(Dec 10 '11 at 00:18)
Lucian Sasu
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