Constrained EM algorithm with projection method
Constrained EM algorithm with projection method
复制标题
DOI：
10.1007/s00180-011-0285-x
复制
发表时间：
2011-10
影响因子：
1.3
通讯作者：
Keiji Takai
中科院分区：
文献类型：
--
作者：
Keiji Takai
本文提出了一种新的步骤称为P-步骤，以处理除了传统的EM算法的线性或非线性等式约束。这个新的步骤很容易实现，首先是因为只有目标函数和约束函数的一阶导数是必要的，其次，因为P-步骤是在常规EM算法之后执行的。由我们的方法产生的估计序列享有一个单调增加的观测似然函数。除了传统的EM算法的两个说明性的例子，我们应用的P-步骤。第一个示例具有线性约束函数。第二个具有非线性约束函数。最后我们证明了在由我们的方法产生的极限点处存在一个Kuhn-Tucker向量。
This paper proposes a new step called the P-step to handle the linear or nonlinear equality constraint in addition to the conventional EM algorithm. This new step is easy to implement, first because only the first derivatives of the object function and the constraint function are necessary, and secondly, because the P-step is carried out after the conventional EM algorithm. The estimate sequence produced by our method enjoys a monotonic increase in the observed likelihood function. We apply the P-step in addition to the conventional EM algorithm to the two illustrative examples. The first example has a linear constraint function. The second has a nonlinear constraint function. We show finally that there exists a Kuhn–Tucker vector at the limit point produced by our method.