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has been cited by the following article:

• TITLE: Quantile Regression Based on Laplacian Manifold Regularizer with the Data Sparsity in l1 Spaces

  AUTHORS: Ru Feng, Shuang Chen, Lanlan Rong

  KEYWORDS: Semi-Supervised Learning, Conditional Quantile Regression, l1-Regularizer, Manifold-Regularizer, Pinball Loss

  JOURNAL NAME: Open Journal of Statistics, Vol.7 No.5, October 23, 2017

  ABSTRACT: In this paper, we consider the regularized learning schemes based on l1-regularizer and pinball loss in a data dependent hypothesis space. The target is the error analysis for the quantile regression learning. There is no regularized condition with the kernel function, excepting continuity and boundness. The graph-based semi-supervised algorithm leads to an extra error term called manifold error. Part of new error bounds and convergence rates are exactly derived with the techniques consisting of l1-empirical covering number and boundness decomposition.