The expectation–maximization (EM) algorithm is a powerful computational technique for maximum likelihood estimation in incomplete data models. When the expectation step cannot be performed in closed form, a stochastic approximation of EM (SAEM) can be used. The convergence of the SAEM toward critical points of the observed likelihood has been proved and its numerical efficiency has been demonstrated. However, sampling from the posterior distribution may be intractable or have a high computational cost. Moreover, despite appealing features, the limit position of this algorithm can strongly depend on its starting one. Sampling from an approximation of the distribution in the expectation phase of the SAEM allows coping with these two issues. This new procedure is referred to as approximated-SAEM and is proved to converge toward critical points of the observed likelihood. Experiments on synthetic and real data highlight the performance of this algorithm in comparison to the SAEM and the EM when feasible.

期望最大化（EM）算法是用于在不完整数据模型中进行最大似然估计的强大计算技术。当期望步骤无法以封闭形式执行时，可以使用EM（SAEM）的随机近似值。已经证明了SAEM朝着观察到的可能性的临界点的收敛性，并且已经证明了其数值效率。但是，从后验分布进行采样可能难以处理或具有较高的计算成本。此外，尽管具有吸引人的功能，但该算法的极限位置可能在很大程度上取决于其起始位置。在SAEM的预期阶段从分布的近似值进行抽样可以解决这两个问题。这种新程序称为“近似SAEM”，并证明已收敛到观察到的似然度的临界点。在可行的情况下，通过合成数据和真实数据进行的实验凸显了该算法与SAEM和EM相比的性能。