标题： 高维时间序列的稀疏组因子分析 显示英文标题

标题： Sparse-Group Factor Analysis for High-Dimensional Time Series

摘要： 因子分析是一种在高维数据中用于降维的广泛使用技术。 然而，因子模型中的一个关键挑战在于潜在因子的可解释性。 一种直观的解释这些因子的方法是通过它们相关的载荷。 刘和王提出了一种新框架，通过稀疏载荷重新定义因子模型以提高可解释性。 在许多高维时间序列应用中，变量表现出自然的群体结构。 基于这一想法，我们的论文通过在载荷矩阵中建模个体稀疏性和群体稀疏性来结合领域知识和先验信息。 这种双重稀疏框架进一步提高了估计因子的可解释性。 我们开发了一个算法来估计载荷矩阵和公共成分，并建立了所得估计量的渐近性质。 模拟研究证明了所提出方法的强大性能，一个实际数据应用说明了结合先验知识如何导致更可解释的结果。 显示英文摘要

摘要： Factor analysis is a widely used technique for dimension reduction in high-dimensional data. However, a key challenge in factor models lies in the interpretability of the latent factors. One intuitive way to interpret these factors is through their associated loadings. Liu and Wang proposed a novel framework that redefines factor models with sparse loadings to enhance interpretability. In many high-dimensional time series applications, variables exhibit natural group structures. Building on this idea, our paper incorporates domain knowledge and prior information by modeling both individual sparsity and group sparsity in the loading matrix. This dual-sparsity framework further improves the interpretability of the estimated factors. We develop an algorithm to estimate both the loading matrix and the common component, and we establish the asymptotic properties of the resulting estimators. Simulation studies demonstrate the strong performance of the proposed method, and a real-data application illustrates how incorporating prior knowledge leads to more interpretable results.