Research map / Learning theory and algorithms / Matrix and tensor methods
Communication-efficient Algorithms for Distributed Stochastic Principal Component Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Average local eigenvectors without sign alignment | Local PCA ERMs · Distributed stochastic PCA | estimation error: \Omega(1/n) | Hurt |
| Align local eigenvector signs to machine 1 before averaging | Local PCA ERMs · Distributed stochastic PCA | estimation error: O\left(\frac{b^2\ln\left(\frac{dm}{p}\right)}{\delta^2 mn}+\frac{ b^4 \ln^2\left(\frac{dm}{p}\right)}{\delta^4 n^2}\righ | Helped |
| Apply Shift-and-Invert with local preconditioning | Distributed PCA · Distributed stochastic PCA | communication rounds: \tilde{O}(\min\{(b/\delta)^{1/2}n^{-1/4},~ m^{1/4}\}) | Helped |
| Use Shift-and-Invert to approximate the centralized ERM | Distributed PCA · Distributed stochastic PCA | estimation error: \epsilon_{\textrm{ERM}}(p))\cdot \left({1 + o(1)}\right) | Helped |
| Use local preconditioning for the linear systems | Shift-and-Invert · Distributed stochastic PCA | communication rounds: \tilde{O}\left(\sqrt{\frac{1}{\delta\sqrt{n}}}\right) | Helped |
| Average local eigenvectors rather than run centralized ERM | Local PCA ERMs · Distributed stochastic PCA | estimation error: \Omega(1/n) | Hurt |
| Align local eigenvector signs before averaging | Local PCA ERMs · Synthetic normal and uniform sampling-based data | estimation error | Helped |
| Average local projection matrices and take their leading eigenvector | Local PCA ERMs · Synthetic data | estimation error | Helped |
| Use sign-fixing aggregation when per-machine sample size is small | Local PCA ERMs · Synthetic data | estimation error | Hurt |
| Replace sign-fixing aggregation with projection-matrix aggregation | Local PCA ERMs · Synthetic data | estimation error | Helped |
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