论文标题
非covex潜在变量模型的一类两次尺度随机EM算法
A Class of Two-Timescale Stochastic EM Algorithms for Nonconvex Latent Variable Models
论文作者
论文摘要
期望最大化（EM）算法是学习潜在变量模型的流行选择。最初已经引入了EM的变体，使用增量更新以扩展到大型数据集，并使用Monte Carlo（MC）近似来绕过大多数非convex模型的潜在数据对潜在数据的棘手条件期望。在本文中，我们提出了一种基于随机更新的两阶段方法的一类称为两种尺度EM方法的方法，以解决潜在变量模型的必需非convex优化任务。我们通过在两个噪声来源中调用方法的每个阶段的差异降低优点来激发双重动态的选择：增量更新和MC近似的索引采样。我们为非convex目标函数建立有限的时间和全局收敛范围。还提供了各种模型上的数值应用，例如用于图像分析的可变形模板或用于药代动力学的非线性模型，以说明我们的发现。
The Expectation-Maximization (EM) algorithm is a popular choice for learning latent variable models. Variants of the EM have been initially introduced, using incremental updates to scale to large datasets, and using Monte Carlo (MC) approximations to bypass the intractable conditional expectation of the latent data for most nonconvex models. In this paper, we propose a general class of methods called Two-Timescale EM Methods based on a two-stage approach of stochastic updates to tackle an essential nonconvex optimization task for latent variable models. We motivate the choice of a double dynamic by invoking the variance reduction virtue of each stage of the method on both sources of noise: the index sampling for the incremental update and the MC approximation. We establish finite-time and global convergence bounds for nonconvex objective functions. Numerical applications on various models such as deformable template for image analysis or nonlinear models for pharmacokinetics are also presented to illustrate our findings.
