Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression
Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression
复制标题
二元混合线性回归的EM算法的全局收敛性
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
C. Caramanis
中科院分区：
文献类型：
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作者：
Jeongyeol Kwon;C. Caramanis
期望最大化算法可能是推断潜在变量问题的最广泛使用的算法。然而，对它的表现在很大程度上仍然缺乏理论上的理解。最近的研究结果表明，对于高斯混合模型，EM具有全局收敛特性。然而，对于混合线性回归，只建立了局部收敛结果，并且只建立了高信噪比区域的结果。我们证明了EM收敛于具有两个分量的混合线性回归(已知它可能不收敛于三个或更多个分量)，而且这种收敛对于随机初始化是成立的。我们的分析表明，EM在混合线性回归中的行为与其在高斯混合模型中的行为非常不同，因此我们的证明需要发展几个新的想法。
The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that EM enjoys global convergence for Gaussian Mixture Models. For Mixed Linear Regression, however, only local convergence results have been established, and those only for the high SNR regime. We show here that EM converges for mixed linear regression with two components (it is known that it may fail to converge for three or more), and moreover that this convergence holds for random initialization. Our analysis reveals that EM exhibits very different behavior in Mixed Linear Regression from its behavior in Gaussian Mixture Models, and hence our proofs require the development of several new ideas.
DOI：
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发表时间：
2016-09
期刊：
ArXiv
影响因子：
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作者：
C. Daskalakis;Christos Tzamos;Manolis Zampetakis
通讯作者：
C. Daskalakis;Christos Tzamos;Manolis Zampetakis