Quantile Regression Based on Laplacian Manifold Regularizer with the Data Sparsity in l1 Spaces - Open Journal of Statistics

OJS > Vol.7 No.5, October 2017

Quantile Regression Based on Laplacian Manifold Regularizer with the Data Sparsity in l1 Spaces ()

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DOI: 10.4236/ojs.2017.75056 714 Downloads 1,364 Views

Author(s)

Ru Feng¹, Shuang Chen^2*, Lanlan Rong¹

Affiliation(s)

¹School of Sciences, Hebei University of Technology, Tianjin, China.
²School of Sciences, Beijing Institute of Petrochemical Technology, Beijing, China.

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.

KEYWORDS

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

Share and Cite:

Feng, R. , Chen, S. and Rong, L. (2017) Quantile Regression Based on Laplacian Manifold Regularizer with the Data Sparsity in l1 Spaces. Open Journal of Statistics, 7, 786-802. doi: 10.4236/ojs.2017.75056.

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