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Many machine learning models are reformulated as optimization problems. Thus, it is important to solve a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness in the ordinary Newton method of(More)
Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate for the exact solution onto that space to get a new estimate. Many vairants of Kacz-marz algorithms are proposed on(More)
In this paper, we study subspace embedding problem and obtain the following results: 1. We extend the results of approximate matrix multiplication from the Frobenius norm to the spectral norm. Assume matrices A and B both have at most r stable rank and˜r rank, respectively. Let S be a subspace embedding matrix with l rows which depends on stable rank, then(More)
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with Today's applications involved in larger and larger dataset, more and more efficient generalized matrix approximation algorithems become a crucially important research(More)
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