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Faster Principal Component Regression and Stable Matrix Chebyshev Approximation
Zeyuan Allen-Zhu, Yuanzhi Li
We solve principal component regression (PCR), up to a multiplicative accuracy , by reducing the problem to black-box calls of ridge regression. Therefore,…
First Efficient Convergence for Streaming k-PCA: a Global, Gap-Free, and Near-Optimal Rate
Zeyuan Allen-Zhu, Yuanzhi Li
We study streaming principal component analysis (PCA), that is to find, in space, the top eigenvectors of a hidden matrix with online vectors drawn…
Doubly Accelerated Methods for Faster CCA and Generalized Eigendecomposition
Zeyuan Allen-Zhu, Yuanzhi Li
We study -GenEV, the problem of finding the top generalized eigenvectors, and -CCA, the problem of finding the top vectors in canonical-correlation analysis. We propo…
LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain
Zeyuan Allen-Zhu, Yuanzhi Li
We study -SVD that is to obtain the first singular vectors of a matrix . Recently, a few breakthroughs have been discovered on -SVD: Musco and Musco [1] proved the fir…
Katyusha: The First Direct Acceleration of Stochastic Gradient Methods
Zeyuan Allen-Zhu
Nesterov's momentum trick is famously known for accelerating gradient descent, and has been proven useful in building fast iterative algorithms. However, in the stochastic setting,…
Variance Reduction for Faster Non-Convex Optimization
Zeyuan Allen-Zhu, Elad Hazan
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem…
Optimal Black-Box Reductions Between Optimization Objectives
Zeyuan Allen-Zhu, Elad Hazan
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification ta…
Exploiting the Structure: Stochastic Gradient Methods Using Raw Clusters
Zeyuan Allen-Zhu, Yang Yuan, Karthik Sridharan
The amount of data available in the world is growing faster than our ability to deal with it. However, if we take advantage of the internal \emph{structure}, data may become much s…