论文标题
潜在变量模型估计的计算：统一的随机近端框架
Computation for Latent Variable Model Estimation: A Unified Stochastic Proximal Framework
论文作者
论文摘要
潜在变量模型一直在心理计量学和相关领域中发挥着核心作用。在许多现代应用中，基于潜在变量模型的推论涉及以下一个或几个特征：（1）存在许多潜在变量，（2）观察到的和潜在变量是连续的，离散的或两者的组合，（3）对参数的约束，以及（4）对参数施加模型Parssimony的惩罚。该估计通常涉及基于边际可能性/伪样的目标功能最大化目标函数，可能对参数的约束和/或惩罚。由于上述功能带来的复杂性，解决此优化问题是高度不平凡的。尽管已经提出了几种有效的算法，但缺乏将所有这些功能考虑在内的统一计算框架。在本文中，我们填补了空白。具体而言，我们为优化问题提供了统一的公式，然后提出了准牛顿随机近端算法。建立了所提出算法的理论特性。在各种设置下，用于潜在可变模型估计的各种设置下的模拟研究显示了计算效率和鲁棒性。
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of many latent variables, (2) the observed and latent variables being continuous, discrete, or a combination of both, (3) constraints on parameters, and (4) penalties on parameters to impose model parsimony. The estimation often involves maximizing an objective function based on a marginal likelihood/pseudo-likelihood, possibly with constraints and/or penalties on parameters. Solving this optimization problem is highly non-trivial, due to the complexities brought by the features mentioned above. Although several efficient algorithms have been proposed, there lacks a unified computational framework that takes all these features into account. In this paper, we fill the gap. Specifically, we provide a unified formulation for the optimization problem and then propose a quasi-Newton stochastic proximal algorithm. Theoretical properties of the proposed algorithms are established. The computational efficiency and robustness are shown by simulation studies under various settings for latent variable model estimation.
