论文标题
掩盖它！二分图在稀疏因子分析中发现可识别性
Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis
论文作者
论文摘要
尽管具有稀疏负载矩阵的因子模型的流行，但很少有人注意对这些模型的正式可识别性，而不是基于标准旋转的标识，例如较低的三角形约束。为了填补这一空白，我们提出了对非零因子负载数量的计数规则，这足以实现因子表示中方差分解的一般唯一性。这是在稀疏矩阵空间的框架和图形和网络理论的一些经典元素的框架中形式化的。此外，我们提供了一种用于验证计数规则的计算高效工具。在贝叶斯稀疏因子分析中，在后处理后绘制后期绘制了我们的实际数据。
Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular constraint. To fill this gap, we present a counting rule on the number of nonzero factor loadings that is sufficient for achieving generic uniqueness of the variance decomposition in the factor representation. This is formalized in the framework of sparse matrix spaces and some classical elements from graph and network theory. Furthermore, we provide a computationally efficient tool for verifying the counting rule. Our methodology is illustrated for real data in the context of post-processing posterior draws in Bayesian sparse factor analysis.
