Joint estimation of high-dimensional spiked covariance matrices via a partially shared subspace

2026-07-09

AI Summary

This work addresses the challenge of high-dimensional covariance estimation under limited sample sizes and the difficulty of effectively integrating related yet heterogeneous auxiliary data. The authors propose a symmetric two-dataset spiked covariance model that, for the first time, rigorously characterizes partially shared subspace structures at arbitrary spectral locations within a high-dimensional asymptotic framework. The method jointly estimates the shared subspace and its rank and derives closed-form optimal pooling weights. Leveraging random matrix theory and proportional growth asymptotics, it fills a critical theoretical gap in covariance estimation for contrastive dimensionality reduction. Experiments demonstrate significant improvements in covariance estimation accuracy and downstream task performance, notably in early-pandemic portfolio construction and glioma gene expression analysis.

Abstract

Statistical analysis of high-dimensional data is often hampered by limited sample sizes, yet auxiliary datasets from related sources are often readily available. When two such datasets share part of their covariance structure, but not all of it, exploiting the shared part can substantially improve estimation. We propose a spiked covariance model that explicitly captures this partial sharing: two datasets share a subspace of unknown rank and arbitrary position in the spectrum, while each retains its own distinct spiked directions. The model treats the two datasets symmetrically and strictly generalizes existing models for shared covariance structure. We develop a complete estimation procedure that includes joint estimation of the shared subspace and its rank, a closed-form pooling weight for combining the two datasets, and asymptotic guarantees derived from random matrix theory in the proportional-growth regime. The framework also resolves a gap in contrastive dimension reduction by providing a principled estimator for high-dimensional settings. We illustrate the methodology on portfolio construction during the early COVID-19 pandemic and on contrastive analysis of brain tumor gene expression.

Problem

• spiked covariance
• high-dimensional data
• shared subspace
• partial sharing
• covariance estimation

Innovation

• spiked covariance model
• partially shared subspace
• joint estimation
• random matrix theory
• contrastive dimension reduction