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- W2955646041 abstract "In this paper we introduce the theory of derivatives of moments and (moment) functionals to represent moment functionals by Gaussian mixtures, characteristic functions of polytopes, and simple functions of polytopes. We study, among other measures, Gaussian mixtures, their reconstruction from moments and especially the number of Gaussians needed to represent moment functionals. We find that there are moment functionals $L:mathbb{R}[x_1,dots,x_n]_{leq 2d}tomathbb{R}$ which can be represented by a sum of $binom{n+2d}{n} - ncdot binom{n+d}{n} + binom{n}{2}$ Gaussians but not less. Hence, for any $dinmathbb{N}$ and $varepsilon>0$ we find an $ninmathbb{N}$ such that $L$ can be represented by a sum of $(1-varepsilon)cdotbinom{n+2d}{n}$ Gaussians but not less. An upper bound is $binom{n+2d}{n}-1$." @default.
- W2955646041 created "2019-07-12" @default.
- W2955646041 creator A5010485476 @default.
- W2955646041 date "2019-06-28" @default.
- W2955646041 modified "2023-10-01" @default.
- W2955646041 title "The multidimensional truncated Moment Problem: Shape and Gaussian Mixture Reconstruction from Derivatives of Moments" @default.
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