论文标题
使用$ l^p $损失和相关推理问题旋转至稀疏负载
Rotation to Sparse Loadings using $L^p$ Losses and Related Inference Problems
论文作者
论文摘要
研究人员已广泛使用探索性因素分析（EFA）来学习多元数据的潜在结构。旋转和正则化估计是EFA中的两类方法，它们通常用于查找可解释的加载矩阵。在本文中，我们提出了一个基于组件的$ l^p $损失功能$（0 <p \ leq 1）$的新的倾斜旋转家族，该旋转与$ l^p $正规估算器密切相关。我们根据提出的旋转方法开发模型选择和选择后推理程序。当真正的负载矩阵稀疏时，就统计准确性和计算成本而言，提出的方法倾向于优于传统旋转和正规估计方法。由于所提出的损失函数是非平滑的，因此我们开发了一种迭代重新加权的梯度投影算法，用于解决优化问题。我们还开发了理论结果，以建立估计，模型选择和选择后推断的统计一致性。我们评估了提出的方法，并通过模拟研究将其与正则化估计和传统旋转方法进行了比较。我们进一步使用五巨头人格评估的应用程序对其进行了说明。
Researchers have widely used exploratory factor analysis (EFA) to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that they often use to find interpretable loading matrices. In this paper we propose a new family of oblique rotations based on component-wise $L^p$ loss functions $(0 < p\leq 1)$ that is closely related to an $L^p$ regularised estimator. We develop model selection and post-selection inference procedures based on the proposed rotation method. When the true loading matrix is sparse, the proposed method tends to outperform traditional rotation and regularised estimation methods in terms of statistical accuracy and computational cost. Since the proposed loss functions are nonsmooth, we develop an iteratively reweighted gradient projection algorithm for solving the optimisation problem. We also develop theoretical results that establish the statistical consistency of the estimation, model selection, and post-selection inference. We evaluate the proposed method and compare it with regularised estimation and traditional rotation methods via simulation studies. We further illustrate it using an application to the Big Five personality assessment.
