Efficient computation of the Fisher information matrix in the EM algorithm
Efficient computation of the Fisher information matrix in the EM algorithm
复制标题
EM算法中Fisher信息矩阵的高效计算
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
J. Spall
中科院分区：
文献类型：
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作者：
Lingyao Meng;J. Spall
期望最大化 (EM) 算法是一种迭代计算方法，用于根据样本数据计算最大似然估计量 (MLE)。当 MLE 可用时，我们自然需要未知参数的 Fisher 信息矩阵（FIM）。然而，EM 算法的局限性之一是 FIM 不是算法的自动副产品。在本文中，我们构建了一个简单的基于蒙特卡罗的方法，仅需要我们从 E 步骤和基本操作获得的函数的梯度值。我们方法的关键部分是利用同时扰动随机逼近方法根据完整数据对数似然函数的条件期望的梯度来估计Hessian矩阵。
The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. When the MLE is available, we naturally want the Fisher information matrix (FIM) of unknown parameters. However, one of the limitations of the EM algorithm is that the FIM is not an automatic by-product of the algorithm. In this paper, we construct a simple Monte Carlo-based method requiring only the gradient values of the function we obtain from the E step and basic operations. The key part of our method is to utilize the simultaneous perturbation stochastic approximation method to estimate the Hessian matrix from the gradient of the conditional expectation of the complete-data log-likelihood function.