Convergence Analysis of Gradient EM for Multi-component Gaussian Mixture
Convergence Analysis of Gradient EM for Multi-component Gaussian Mixture
复制标题
多组分高斯混合物梯度EM的收敛性分析
DOI：
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发表时间：
2017
期刊：
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通讯作者：
Purnamrita Sarkar
中科院分区：
文献类型：
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作者：
Bowei Yan;Mingzhang Yin;Purnamrita Sarkar
在本文中，我们研究了对于一般数目的聚类和混合系数的高斯混合模型，梯度期望-最大化算法cite{lange1995梯度}的收敛性。我们推导了收敛速率取决于混合系数、真中心之间的最小和最大成对距离以及分量的维数和数量；得到近似最优的局部收缩半径。虽然最近有一些值得注意的工作，在两个相等的混合对称GMM中推导出EM的局部收敛率，但在更一般的情况下，推导需要结构上不同的和非平凡的参数。我们使用学习理论和经验过程的最新工具来实现我们的理论结果。
In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients. We derive the convergence rate depending on the mixing coefficients, minimum and maximum pairwise distances between the true centers and dimensionality and number of components; and obtain a near-optimal local contraction radius. While there have been some recent notable works that derive local convergence rates for EM in the two equal mixture symmetric GMM, in the more general case, the derivations need structurally different and non-trivial arguments. We use recent tools from learning theory and empirical processes to achieve our theoretical results.