We present a federated, asynchronous, and $(\varepsilon, \delta)$-differentially private algorithm for $\PCA$ in the memory-limited setting.

Weaknesses: The error of the rank r subspace given by recursively merging local updates is not stated concretely. I would expect the analyis of error between the subspace given by this algorithm after observing n data points and the subspace spanned by leading r singular vectors of the full dataset. Can the authors explain whether that is not feasible in this setting? When performing input perturbation for privacy, since the paper discusses PCA with adaptive rank'r', I would expect an analysis of the error in subspace spanned by leading r eigenvectors given by the algorithm as opposed to the error in first eigenvector. In line 190, it claims the memory requirement is O(cdn) as opposed to O(d 2) in mod-sulq.

Four knowledgeable reviewers support acceptance of this paper, in view of the novelty of the differentially private, federated PCA algorithm and the strength of the analysis provided for its variants. I concur with the reviewers. The reviewers pointed out issues with the clarity of the paper, and the authors promised several edits to address this issue in their rebuttal; please implement these changes.

We present a federated, asynchronous, and (\varepsilon, \delta) -differentially private algorithm for \PCA in the memory-limited setting.