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We present a series of closed-form maximum entropy upper bounds for thedifferential entropy of a continuous univariate random variable and study theproperties of that series. We then show how to use those generic bounds forupper bounding the differential entropy of Gaussian mixture models. Thisrequires to calculate the raw moments and raw absolute moments of Gaussianmixtures in closed-form that may also be handy in statistical machine learningand information theory. We report on our experiments and discuss on thetightness of those bounds.

A series of maximum entropy upper bounds of the differential entropy