GAUSSIAN MIXTURE MODELS AND VC DIMENSIONS

Abstract

We will establish the VC dimension of the class of translated ellipsoids in d-dimensional Euclidean space is between (d/2+1)2 and (6.53486 ・ ・ ・ )(d2+3d). By this, (d/2+1)2 turns out to be a lower bound of the VC dimension of the concept class that N-component Gaussian mixture models induce through maximum likelihood estimate.