Quantile Regression Based on Laplacian Manifold Regularizer with the Data Sparsity in <i>l</i>1 Spaces

• 作者: Lanlan Rong Ru Feng Shuang Chen
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: SEMI-SUPERVISED Learning Conditional QUANTILE Regression l1-Regularizer Manifold-Regularizer Pinball Loss
• 年，卷（期）: 2017,（5）
• 页码范围: 786-802
• 页数: 17页
• 分类号: O1

摘要

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.