VC dimension of ellipsoids
classification
🧮 math.CO
cs.LGstat.ML
keywords
dimensionclassd-dimensionalellipsoidsgaussianmixturedimensionalellipsoid
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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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