论文标题
低SNR高斯混合模型中的可能性最大化和力矩匹配
Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models
论文作者
论文摘要
我们得出了在低信号到噪声方面具有相等协方差矩阵的高斯混合模型（GMM）对数可能性的渐近扩展。该扩展揭示了参数估计的两种类型的算法之间的紧密联系：矩和似然优化算法（例如期望最大化（EM））的方法。我们表明，低SNR制度中的似然优化将减少到一系列最小二乘优化问题，这些问题与估计的矩与地面真相矩矩矩相匹配。这种连接是对EM分析和在各种模型中最大似然估计的垫脚石。低SNR混合物模型研究的激励应用是冷冻电子显微镜数据，可以将其模拟为GMM，并在混合物中心施加的代数约束。我们讨论了我们扩展到代数约束GMM的应用，以及其他感兴趣的示例模型。
We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for parameter estimation: the method of moments and likelihood optimizing algorithms such as Expectation-Maximization (EM). We show that likelihood optimization in the low SNR regime reduces to a sequence of least squares optimization problems that match the moments of the estimate to the ground truth moments one by one. This connection is a stepping stone toward the analysis of EM and maximum likelihood estimation in a wide range of models. A motivating application for the study of low SNR mixture models is cryo-electron microscopy data, which can be modeled as a GMM with algebraic constraints imposed on the mixture centers. We discuss the application of our expansion to algebraically constrained GMMs, among other example models of interest.
