Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically difficult to obtain tight lower bounds for mixtures. Exploiting a connection between total variation distance and the characteristic function of the mixture, we provide fairly tight functional approximations. This enables us to derive new lower bounds on the total variation distance between pairs of two-component Gaussian mixtures that have a shared covariance matrix.
翻译：在统计和学习理论中广泛研究了高斯高斯高斯高斯高地分布的混合体。虽然在分布学习的样本复杂性中,总变差距离是自然的,但从分析上看很难获得混合物的紧凑下限。利用总变差距离与混合物特性功能之间的联系,我们提供相当紧凑的功能近似值。这使我们能够从具有共同共变量矩阵的两种成分高斯混合体的配对之间总变差距离上得出新的更低的界限。
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