VC dimension of ellipsoids

Mathematics – Combinatorics

Scientific paper

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Scientific paper

We will establish that the VC dimension of the class of d-dimensional
ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component
d-dimensional Gaussian mixture models induces a geometric class having VC
dimension at least N(d^2+3d)/2.
Keywords: VC dimension; finite dimensional ellipsoid; Gaussian mixture model

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