期望最大化算法
算法
单调函数
数学
最大化
似然函数
数学优化
趋同(经济学)
收敛速度
单调多边形
计算机科学
估计理论
最大似然
统计
数学分析
频道(广播)
计算机网络
几何学
经济
经济增长
作者
Jeffrey A. Fessler,Alfred O. Hero
摘要
The expectation-maximization (EM) method can facilitate maximizing likelihood functions that arise in statistical estimation problems. In the classical EM paradigm, one iteratively maximizes the conditional log-likelihood of a single unobservable complete data space, rather than maximizing the intractable likelihood function for the measured or incomplete data. EM algorithms update all parameters simultaneously, which has two drawbacks: 1) slow convergence, and 2) difficult maximization steps due to coupling when smoothness penalties are used. The paper describes the space-alternating generalized EM (SAGE) method, which updates the parameters sequentially by alternating between several small hidden-data spaces defined by the algorithm designer. The authors prove that the sequence of estimates monotonically increases the penalized-likelihood objective, derive asymptotic convergence rates, and provide sufficient conditions for monotone convergence in norm. Two signal processing applications illustrate the method: estimation of superimposed signals in Gaussian noise, and image reconstruction from Poisson measurements. In both applications, the SAGE algorithms easily accommodate smoothness penalties and converge faster than the EM algorithms.< >
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