Information Geometry of smooth densities on the Gaussian space: Poincaré inequalities

02/28/2020

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by   Giovanni Pistone, et al.

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We derive bounds for the Orlicz norm of the deviation of a random variable defined on R^n from its Gaussian mean value. The random variables are assumed to be smooth and the bound itself depends on the Orlicz norm of the gradient. Applications to non-parametric Information Geometry are discussed.