Analysis of random target subspaces and dependent data sources

Establish a full theoretical treatment of augmented James–Stein eigenvector and eigenspace estimation when the target subspace is random, including target subspaces estimated from another data source and multiple potentially dependent data sources.

Background

The paper’s theoretical analysis assumes that the target subspace is deterministic. In applications, however, target directions may be estimated from another dataset or learned from related populations, making the target subspace random and potentially dependent on the data used for the eigenvector estimation procedure.

The authors state that their framework could serve as a starting point for an analysis conditional on the random target, but they do not resolve the unconditional theory for multiple potentially dependent data sources. This is therefore an explicitly identified unresolved problem for extending the proposed augmented James–Stein methodology beyond deterministic targets.