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Poster
Exponentially convergent stochastic k-PCA without variance reduction
Cheng Tang

Thu Dec 10:45 AM -- 12:45 PM PST @ East Exhibition Hall B + C #200

We present Matrix Krasulina, an algorithm for online k-PCA, by gen- eralizing the classic Krasulina’s method (Krasulina, 1969) from vector to matrix case. We show, both theoretically and empirically, that the algorithm naturally adapts to data low-rankness and converges exponentially fast to the ground-truth principal subspace. Notably, our result suggests that despite various recent efforts to accelerate the convergence of stochastic-gradient based methods by adding a O(n)-time variance reduction step, for the k- PCA problem, a truly online SGD variant suffices to achieve exponential convergence on intrinsically low-rank data.

Author Information

Cheng Tang (Amazon)

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