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math.ST2015★ 1 cited
On the Robustness of Regularized Pairwise Learning Methods Based on Kernels
Andreas Christmann, Ding-Xuan Zhou
Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) meth…
math.ST2015★ 6 cited
Minimax Optimal Rates of Estimation in High Dimensional Additive Models: Universal Phase Transition
Ming Yuan, Ding-Xuan Zhou
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting ph…
math.ST2010★ 41 cited
Learning gradients on manifolds
Sayan Mukherjee, Qiang Wu, Ding-Xuan Zhou
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on man…