基于散度估计演算的两个迭代邻近点算法及其在混合模型中的应用
Two Iterative Proximal-Point Algorithms for the Calculus of Divergence-based Estimators with Application to Mixture Models
摘要：
从期望最大化算法导出的估计是不稳健的，因为它们是基于似然函数的最大化。在期望最大化算法的基础上，提出了一种以最小化发散准则为目标的近似点算法。由此产生的估计一般是强大的离群值和误指定。EM型邻近点算法也被引入，以产生混合模型的鲁棒估计。这两个算法的收敛性。我们放松了可识别性条件施加在文献中的近端项，这是一个条件，一般不满足混合模型。所介绍的算法的收敛性进行了讨论的两个组件的威布尔混合和两个组件的高斯混合，需要一个条件上的初始化的期望最大化算法，以便后者收敛。使用不同的统计偏差的混合模型上的模拟，以确认我们的工作的有效性和鲁棒性的估计对离群值相比，期望最大化算法。
英文摘要：
Estimators derived from an EM algorithm are not robust since they are based on the maximization of the likelihood function. We propose a proximal-point algorithm based on the EM algorithm which aim to minimize a divergence criterion. Resulting estimators are generally robust against outliers and misspecification. An EM-type proximal-point algorithm is also introduced in order to produce robust estimators for mixture models. Convergence properties of the two algorithms are treated. We relax an identifiability condition imposed on the proximal term in the literature; a condition which is generally not fulfilled by mixture models. The convergence of the introduced algorithms is discussed on a two-component Weibull mixture and a two-component Gaussian mixture entailing a condition on the initialization of the EM algorithm in order for the later to converge. Simulations on mixture models using different statistical divergences are provided to confirm the validity of our work and the robustness of the resulting estimators against outliers in comparison to the EM algorithm.
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