径向分布的测度集中与统计建模的结果
Concentration of Measure for Radial Distributions and Consequences for Statistical Modeling
摘要：
受高维统计问题的启发，如分类和聚类的混合建模，我们考虑了径向密度随维数增加的行为。我们建立了一种形式的浓度的措施，甚至依分布收敛，在额外的假设。这将众所周知的正态分布的行为（其集中在半径为维度平方根的球体周围）扩展到其他径向密度。我们得出了一些可能的后果，在高维统计建模，包括高斯混合物的可能的普适性属性。
英文摘要：
Motivated by problems in high-dimensional statistics such as mixture modeling for classification and clustering, we consider the behavior of radial densities as the dimension increases. We establish a form of concentration of measure, and even a convergence in distribution, under additional assumptions. This extends the well-known behavior of the normal distribution (its concentration around the sphere of radius square-root of the dimension) to other radial densities. We draw some possible consequences for statistical modeling in high-dimensions, including a possible universality property of Gaussian mixtures.
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