Statistical performance of quantile tensor regression with convex regularization

Wenqi Lu, Zhongyi Zhu, Rui Li and Heng Lian

Journal of Multivariate Analysis, 2024, vol. 200, issue C

Abstract: In this paper, we consider high-dimensional quantile tensor regression using a general convex decomposable regularizer and analyze the statistical performances of the estimator. The rates are stated in terms of the intrinsic dimension of the estimation problem, which is, roughly speaking, the dimension of the smallest subspace that contains the true coefficient. Previously, convex regularized tensor regression has been studied with a least squares loss, Gaussian tensorial predictors and Gaussian errors, with rates that depend on the Gaussian width of a convex set. Our results extend the previous work to nonsmooth quantile loss. To deal with the non-Gaussian setting, we use the concept of Rademacher complexity with appropriate concentration inequalities instead of the Gaussian width. For the multi-linear nuclear norm penalty, our Orlicz norm bound for the operator norm of a random matrix may be of independent interest. We validate the theoretical guarantees in numerical experiments. We also demonstrate advantage of quantile regression over mean regression, and compare the performance of convex regularization method and nonconvex decomposition method in solving quantile tensor regression problem in simulation studies.

Keywords: Convex optimization; Quantile regression; Risk bound; Tensor estimation (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X23000957
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:200:y:2024:i:c:s0047259x23000957

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2023.105249

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().