B0732
Title: On varimax asymptotics in network models and spectral methods for dimensionality reduction
Authors: Joshua Cape - University of Wisconsin, Madison (United States) [presenting]
Abstract: Varimax factor rotations, while popular among practitioners in psychology and statistics since being introduced by H. Kaiser, have historically been viewed with scepticism and suspicion by some theoreticians and mathematical statisticians. Now, work by K. Rohe and M. Zeng 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. This newfound understanding of varimax rotations is built by developing further connections to network analysis and spectral methods rooted in entrywise matrix perturbation analysis. Concretely, the asymptotic multivariate normality of vectors is established in varimax-transformed Euclidean point clouds that represent low-dimensional node embeddings in certain latent space random graph models. Related concepts, including network sparsity, data denoising, and the role of matrix rank are addressed 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 nonparametric techniques. Numerical examples illustrate the findings and supplement our discussion.
