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.

翻译：因子分析是高维数据降维中广泛使用的技术。然而，因子模型的一个关键挑战在于潜在因子的可解释性。解释这些因子的一种直观方式是通过其关联的载荷。Liu和Wang提出了一个新颖框架，通过重新定义具有稀疏载荷的因子模型来增强可解释性。在许多高维时间序列应用中，变量展现出自然的组结构。基于这一思想，本文通过在载荷矩阵中同时建模个体稀疏性和组稀疏性，融入了领域知识和先验信息。这种双重稀疏框架进一步提升了估计因子的可解释性。我们开发了一种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方法的优异性能，实际数据应用展示了融入先验知识如何带来更具可解释性的结果。