Symmetry-Aware Convex Shrinkage for High-Dimensional Covariance Estimation
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910228192165888 |
|---|---|
| author | Thornton, Mitchell A. |
| author_facet | Thornton, Mitchell A. |
| contents | We develop a class of data-adaptive shrinkage estimators for high-dimensional covariance estimation in which the shrinkage target is a Reynolds projection of the sample covariance under a finite symmetry group selected from a candidate library by held-out predictive performance. The class generalizes the convex shrinkage estimator of Ledoit and Wolf by replacing the scalar-identity target with a structured target derived from a symmetry group when one is available, and generalizes the group-symmetric maximum-likelihood estimator of Shah and Chandrasekaran by combining structural targeting with adaptive convex shrinkage and by selecting the group from data rather than treating it as prespecified. A two-tier procedure performs the group selection: a universal per-candidate evaluation based on held-out negative log-likelihood, optionally preceded by a domain-specific step that constructs the candidate library from structural priors. We establish a finite-sample regret bound for the held-out calibration of the convex combination weight, an oracle inequality for the data-driven group selection, and a quantitative sufficient-match condition under which the proposed estimator dominates Ledoit-Wolf shrinkage in Frobenius mean-squared error. The procedure is illustrated on six real-data problems spanning finance (S&P~500 daily returns), climate (NOAA OISST sea-surface temperature anomalies), genomics (TCGA-BRCA gene expression), radio signal processing (RadioML 2018.A), astronomical imaging (Galaxy10 DECaLS), and natural image patches (CIFAR-10 with a CIFAR-10.1 distribution-shift companion). An empirical comparison is also made against the Bayesian permutation-symmetry estimator of Chojecki and colleagues. Outside the few-shot regime, where structural priors carry the most information per observation, Ledoit-Wolf shrinkage remains the appropriate baseline. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17111 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry-Aware Convex Shrinkage for High-Dimensional Covariance Estimation Thornton, Mitchell A. Methodology Information Theory Signal Processing We develop a class of data-adaptive shrinkage estimators for high-dimensional covariance estimation in which the shrinkage target is a Reynolds projection of the sample covariance under a finite symmetry group selected from a candidate library by held-out predictive performance. The class generalizes the convex shrinkage estimator of Ledoit and Wolf by replacing the scalar-identity target with a structured target derived from a symmetry group when one is available, and generalizes the group-symmetric maximum-likelihood estimator of Shah and Chandrasekaran by combining structural targeting with adaptive convex shrinkage and by selecting the group from data rather than treating it as prespecified. A two-tier procedure performs the group selection: a universal per-candidate evaluation based on held-out negative log-likelihood, optionally preceded by a domain-specific step that constructs the candidate library from structural priors. We establish a finite-sample regret bound for the held-out calibration of the convex combination weight, an oracle inequality for the data-driven group selection, and a quantitative sufficient-match condition under which the proposed estimator dominates Ledoit-Wolf shrinkage in Frobenius mean-squared error. The procedure is illustrated on six real-data problems spanning finance (S&P~500 daily returns), climate (NOAA OISST sea-surface temperature anomalies), genomics (TCGA-BRCA gene expression), radio signal processing (RadioML 2018.A), astronomical imaging (Galaxy10 DECaLS), and natural image patches (CIFAR-10 with a CIFAR-10.1 distribution-shift companion). An empirical comparison is also made against the Bayesian permutation-symmetry estimator of Chojecki and colleagues. Outside the few-shot regime, where structural priors carry the most information per observation, Ledoit-Wolf shrinkage remains the appropriate baseline. |
| title | Symmetry-Aware Convex Shrinkage for High-Dimensional Covariance Estimation |
| topic | Methodology Information Theory Signal Processing |
| url | https://arxiv.org/abs/2605.17111 |