Transfer Learning for Linear Discriminant Analysis with a Shared Classification Signal

This paper studies transfer learning for linear discriminant analysis in high-dimensional two-class classification.

We consider one target domain and several source domains, where the mean difference in each domain is decomposed into a deterministic common component and a domain-specific random deviation.

The common component represents a shared classification signal across domains, while the random deviation captures domain-specific heterogeneity.

Under spiked covariance models, we derive deterministic limits for the target-domain Gaussian-calibrated error of weighted transfer classifiers under both homogeneous and heterogeneous covariance settings.

These limits quantify the effects of the shared signal, domain-specific variation, dimension-to-sample-size ratios, and spike structures on transfer performance.

They further lead to oracle transfer weights and consistent data-driven plug-in estimators.

We also characterize the intercept bias induced by unbalanced target-domain class sample sizes and provide an asymptotically optimal correction.