Ascent-based Monte Carlo expectation-maximization
Ascent-based Monte Carlo expectation-maximization
复制标题
DOI：
10.1111/j.1467-9868.2005.00499.x
复制
发表时间：
2005-01-01
影响因子：
5.8
通讯作者：
Jones, GL
中科院分区：
文献类型：
--
作者：
Caffo, BS;Jank, W;Jones, GL
期望最大化（EM）算法是一个流行的工具，最大化似然函数的缺失数据的存在。不幸的是，EM往往需要评估的分析棘手和高维积分。蒙特卡罗EM（Monte Carlo EM）算法是EM的自然扩展，它采用蒙特卡罗方法来估计相关积分。通常，当算法接近收敛时，需要非常大的Monte Carlo样本量来在可接受的公差内估计这些积分。即使这个样本量在MCEM的实现开始时是已知的，在所有迭代中使用它也是浪费的，特别是当精确的起始值不可用时。我们提出了一个数据驱动的策略来控制蒙特卡罗资源在MCEM。该算法改进了类似的现有方法恢复EM的上升（即似然增加）属性具有高概率，更强大的用户定义的输入和处理经典的Monte Carlo和马尔可夫链Monte Carlo方法在一个共同的框架内的效果。由于这些属性中的第一个，我们将该算法称为“基于上升的MCEM”。我们将基于上升的MCEM应用于各种示例，包括用于显著加速确定性EM收敛的示例。
The expectation-maximization (EM) algorithm is a popular tool for maximizing likelihood functions in the presence of missing data. Unfortunately, EM often requires the evaluation of analytically intractable and high dimensional integrals. The Monte Carlo EM (MCEM) algorithm is the natural extension of EM that employs Monte Carlo methods to estimate the relevant integrals. Typically, a very large Monte Carlo sample size is required to estimate these integrals within an acceptable tolerance when the algorithm is near convergence. Even if this sample size were known at the onset of implementation of MCEM, its use throughout all iterations is wasteful, especially when accurate starting values are not available. We propose a data-driven strategy for controlling Monte Carlo resources in MCEM. The algorithm proposed improves on similar existing methods by recovering EM's ascent (i.e. likelihood increasing) property with high probability, being more robust to the effect of user-defined inputs and handling classical Monte Carlo and Markov chain Monte Carlo methods within a common framework. Because of the first of these properties we refer to the algorithm as 'ascent-based MCEM'. We apply ascent-based MCEM to a variety of examples, including one where it is used to accelerate the convergence of deterministic EM dramatically.