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What is Learnable in Valiant's Theory of the Learnable? 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Moment ideals of local Dirac mixtures
Alexandros Grosdos Koutsoumpelias, Markus Wageringel · 2018-09-26 · via math.ST updates on arXiv.org

In this paper we study ideals arising from moments of local Dirac measures and their mixtures. We provide generators for the case of first order local Diracs and explain how to obtain the moment ideal of the Pareto distribution from them. We then use elimination theory and Prony's method for parameter estimation of finite mixtures. Our results are showcased with applications in signal processing and statistics. We highlight the natural connections to algebraic statistics, combinatorics and applications in analysis throughout the paper.