椭球的VC维数

摘要：

我们将建立d维椭球类的VC维数为（d^2+3d）/2，并且N分量d维高斯混合模型的最大似然估计导出VC维数至少为N（d^2+3d）/2的几何类。关键词：VC维;有限维椭球;高斯混合模型

英文摘要：

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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