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

arXiv: https://arxiv.org/abs/2607.08123 · HTML: https://mlsanity.com/paper/2607.08123/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control](https://mlsanity.com/paper/2010.11037/) (2020)
- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Personalized PCA: Decoupling Shared and Unique Features](https://mlsanity.com/paper/2207.08041/) (2022)
- [Unsupervised learning with contrastive latent variable models](https://mlsanity.com/paper/1811.06094/) (2018)
- [Estimation of the number of spiked eigenvalues in a covariance matrix by bulk eigenvalue matching analysis](https://mlsanity.com/paper/2006.00436/) (2020)
- [Knowledge Transfer across Multiple Principal Component Analysis Studies](https://mlsanity.com/paper/2403.07431/) (2024)
- [TL-PCA: Transfer Learning of Principal Component Analysis](https://mlsanity.com/paper/2410.10805/) (2024)
- [Shared Subspace Models for Multi-Group Covariance Estimation](https://mlsanity.com/paper/1607.03045/) (2016)
- [Transfer learning for tensor Gaussian graphical models](https://mlsanity.com/paper/2211.09391/) (2022)
- [Contrastive Dimension Reduction: A Systematic Review](https://mlsanity.com/paper/2510.11847/) (2025)

## Built on by (most cited first, 1 of 1)

- [Bias-Corrected Subspace Intersection: Minimax-Optimal Shared Subspace Estimation in Multi-View Data](https://mlsanity.com/paper/2609.05617/) (2026)

## Abstract (arXiv)

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.