On varimax asymptotics in network models and spectral methods for dimensionality reduction

• 成果类型: Article
• 署名作者: Cape, J.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad061
• 发表日期: 2024
• 关键词: eigenvectors

摘要

Varimax factor rotations, while popular among practitioners in psychology and statistics since being introduced by , have historically been viewed with skepticism and suspicion by some theoreticians and mathematical statisticians. Now, work by provides new, fundamental insight: varimax rotations provably perform statistical estimation in certain classes of latent variable models when paired with spectral-based matrix truncations for dimensionality reduction. We build on this new-found understanding of varimax rotations by developing further connections to network analysis and spectral methods rooted in entrywise matrix perturbation analysis. Concretely, this paper establishes the asymptotic multivariate normality of vectors in varimax-transformed Euclidean point clouds that represent low-dimensional node embeddings in certain latent space random graph models. We address related concepts including network sparsity, data denoising and the role of matrix rank in latent variable parameterizations. Collectively, these findings, at the confluence of classical and contemporary multivariate analysis, reinforce methodology and inference procedures grounded in matrix factorization-based techniques. Numerical examples illustrate our findings and supplement our discussion.