This work describes a computationally efficient and statistically consistent moment-based estimator for mixture models under natural non-degeneracy and noise conditions. The estimator assumes that (i) the component means are linearly independent, and (ii) the noise covariance is the same for each component, and is either known or (unknown and) spherical. Under these conditions, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, without additional minimum separation assumptions needed by previous computationally efficient estimation procedures. This implies that computational and information-theoretic barriers to efficient estimation of mixture models are precluded by the non-degeneracy and noise conditions. Some connections are made to estimation problems related to independent component analysis.

本研究提供了一种计算效率高、统计一致的基于矩的混合高斯估计算法，通过简单的谱分解技术，无需额外的最小分离条件，在一般位置上获取成分均值的低阶观测矩，从而通过排除计算和信息理论方面的障碍以便混合模型的高效估计，当混合成分具有一般位置和球形协方差时，与独立成分分析相关的估计问题得到了一些联系。

学习球形高斯混合模型：矩方法与谱分解