Papers › Efficient Convex Relaxations for Streaming PCA
Efficient Convex Relaxations for Streaming PCA
Raman Arora, Teodor Vanislavov Marinov
We revisit two algorithms, matrix stochastic gradient (MSG) and ℓ₂-regularized MSG (RMSG), that are instances of stochastic gradient descent (SGD) on a convex relaxation to principal component analysis (PCA). These algorithms have been shown to outperform Oja’s algorithm, empirically, in terms of the iteration complexity, and to have runtime comparable with Oja’s. However, these findings are not supported by existing theoretical results. While the iteration complexity bound for ℓ₂-RMSG was recently shown to match that of Oja’s algorithm, its theoretical efficiency was left as an open problem. In this work, we give improved bounds on per iteration cost of mini-batched variants of both MSG and ℓ₂-RMSG and arrive at an algorithm with total computational complexity matching that of Oja's algorithm.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections