Title: Principal subspace analysis for high-dimensional compositional data
Authors: Jingru Zhang - Peking University (China)
Wei Lin - Peking University (China) [presenting]
Abstract: Dimension reduction for high-dimensional compositional data plays an important role in many scientific studies, where the principal subspace of the basis covariance matrix is the parameter of interest. However, in practice, the basis variables are latent and rarely observed. The fact that the observed compositions lie in a simplex renders standard techniques inappropriate. To address this challenging problem, we relate the basis covariance to the centered log-ratio compositional covariance. We prove that the principal subspace of the basis covariance matrix is approximately identifiable as the dimensionality tends to infinity under some subspace sparsity assumptions, and derive nonasymptotic error bounds for the subspace estimation. Our theoretical analysis shows that the sparsity assumption not only helps to identify the principal subspace, but also benefits the estimation in high-dimensional settings. Moreover, we develop efficient proximal ADMM algorithms for solving the proposed nonconvex and nonsmooth optimization problems. Simulation results demonstrate that the performance of the proposed methods is nearly as good as the oracle method and significantly superior to those based on different transformations.