FedFask: Fast Sketching Distributed PCA for Large-Scale Federated Data
Bibliographic record
Abstract
We study distributed principal component analysis (PCA) for large-scale federated data when the sample size $n$n and dimension $d$d are both ultra-large. This type of data is currently very common, but faces numerous challenges in PCA learning, such as communication overhead and computational complexity. We develop a new algorithm ${\mathsf {FedFask}}$FedFask (Fast Sketching for Federated learning) with lower communication cost $O(dr)$O(dr) and lower computational complexity $O(d(np/m+p^{2}+r^{2}))$O(d(np/m+p2+r2)), where $m$m is the number of workers, $r$r is the rank of matrix, $p$p is the dimension of sketched column space, and $r\leq p\ll d$r≤p≪d. In ${\mathsf {FedFask}}$FedFask, we adopt and develop technologies such as fast sketching, alignments with orthogonal Procrustes Fixing, and matrix Stiefel manifold via Kolmogorov-Nagumo-type average. Thus, ${\mathsf {FedFask}}$FedFask has a higher accuracy, lower stochastic variation, and best representation of multiple randomly projected eigenspaces, and avoids the orthogonal ambiguity of eigenspaces. We show that ${\mathsf {FedFask}}$FedFask achieves the same rate of learning $O\left(\frac{\kappa _{r}r}{\lambda _{r}}\sqrt{\frac{r^{*}}{n}}\right)$Oκrrλrr*n as the centralized PCA uses all data, and tolerates more workers to parallel acceleration computation. We conduct extensive experiments to demonstrate the effectiveness of ${\mathsf {FedFask}}$FedFask.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".