The method of moments is a statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding identifiability asks how many moment equations are needed to get finitely many solutions and how many solutions there are. We answer this question for classes of Gaussian mixture models using the tools of polyhedral geometry. Using these results, we present an algorithm that performs parameter recovery, and therefore density estimation, for high dimensional Gaussian mixture models that scales linearly in the dimension.

翻译：时间方法是一种密度估计的统计技术,它解决了用来估计未知分布参数的瞬时方程系统。一个对理解可识别性至关重要的根本问题在于需要多少分钟方程才能找到有限的多个解决方案和有多少个解决方案。我们用多角度几何几何工具回答高斯混合模型类别的问题。我们利用这些结果,为高斯高斯高斯高斯高斯高斯高斯高斯高斯高斯高原混合物模型提供了一种算法,用于进行参数恢复,从而进行密度估计,在维度上以线性标度标定高斯高斯高斯混合模型。