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arXiv

Hierarchical Spectral Shrinkage (HSS) beats separate, fully pooled, and shared-subspace estimators on synthetic experiments and multi-study gene-expression data

The authors introduce Hierarchical Spectral Shrinkage (HSS), an empirical-Bayes framework that shrinks each task's leading spectral directions toward a data-adaptively learned common basis with shrinkage varying across tasks and spectral components, yielding the posterior mean of singular vectors in a surrogate Bayesian regression; across synthetic experiments and three immune-cell gene-expression datasets (sample sizes 156, 628, 146), HSS improves estimation accuracy and out-of-sample performance over separate, fully pooled, and shared-subspace approaches.