VC dimension of ellipsoids (1109.4347v1)

Published 20 Sep 2011 in math.CO, cs.LG, and stat.ML

Abstract: 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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