Analysis of stopping criteria for the EM algorithm in the context of patient grouping according to length of stay

Revlin Abbi, E. El-Darzi, C. Vasilakis, P. Millard
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引用次数: 21

Abstract

The expectation maximisation (EM) algorithm is an iterative maximum likelihood procedure often used for estimating the parameters of a mixture model. Theoretically, increases in the likelihood function are guaranteed as the algorithm iteratively improves upon previously derived parameter estimates. The algorithm is considered to converge when all parameter estimates become stable and no further improvements can be made to the likelihood value. However, to reduce computational time, it is often common practice for the algorithm to be stopped before complete convergence using heuristic approaches. In this paper, we consider various stopping criteria and evaluate their effect on fitting Gaussian mixture models (GMMs) to patient length of stay (LOS) data. Although the GMM can be successfully fitted to positively skewed data such as LOS, the fitting procedure often requires many iterations of the EM algorithm. To our knowledge, no previous study has evaluated the effect of different stopping criteria on fitting GMMs to skewed distributions. Hence, the aim of this paper is to evaluate the effect of various stopping criteria in order to select and justify their use within a patient spell classification methodology. Results illustrate that criteria based on the difference in the likelihood value and on the GMM parameters may not always be a good indicator for stopping the algorithm. In fact we show that the values of the difference in the variance parameters should be used instead, as these parameters are the last to stabilise. In addition, we also specify threshold values for the other stopping criteria.
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基于住院时间分组的EM算法停止标准分析
期望最大化算法是一种迭代的极大似然过程,常用于估计混合模型的参数。从理论上讲,随着算法在先前导出的参数估计的基础上迭代改进,可以保证似然函数的增加。当所有参数估计都趋于稳定,且无法对似然值进行进一步改进时,认为算法收敛。然而,为了减少计算时间,通常的做法是使用启发式方法在算法完全收敛之前停止。在本文中,我们考虑了各种停止标准,并评估了它们对高斯混合模型(GMMs)拟合患者住院时间(LOS)数据的影响。虽然GMM可以成功地拟合到正偏斜数据,如LOS,但拟合过程通常需要EM算法的多次迭代。据我们所知,以前没有研究评估过不同的停止标准对偏态分布拟合GMMs的影响。因此,本文的目的是评估各种停止标准的效果,以便选择和证明他们在病人法术分类方法中的使用。结果表明,基于似然值和GMM参数差异的准则可能并不总是停止算法的良好指标。事实上,我们表明应该使用方差参数的差值,因为这些参数是最后稳定的。此外,我们还为其他停止准则指定了阈值。
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