A copula-based compressed principal component analysis for high-dimensional heavy-tailed data

To address the challenges posed by non-Gaussianity and dimensionality in high-dimensional stochastic systems, this study proposes a Copula-based compressed principal component analysis (CPCA) framework. Designed to address the inadequate representation of extreme tail characteristics and the susceptibility to numerical oscillations in conventional CPCA, the proposed mixed-parameter strategy is grounded in Sklar’s theorem. Specifically, the construction of the joint distribution is decomposed into three progressive stages: refined modeling of marginal tails using extreme value theory (EVT), decoupling of dependence structures via Copula methods, and subsequent residual correction within the mapped Gaussian latent space. Numerical experiments validate that the proposed approach maintains the baseline accuracy of conventional CPCA on standard benchmarks. Notably, in heavy-tailed simulations, it significantly enhances tail resolution without compromising the capture of global structures. These results confirm the framework’s robustness for high-dimensional non-Gaussian modeling.