Nonsparse Learning with Latent Variables

Zemin Zheng (), Jinchi Lv () and Wei Lin ()
Additional contact information
Zemin Zheng: International Institute of Finance, School of Management, University of Science and Technology of China, Hefei 230026, China
Jinchi Lv: Marshall School of Business, University of Southern California, Los Angeles, California 90089
Wei Lin: School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing 100871, China

Operations Research, 2021, vol. 69, issue 1, 346-359

Abstract: As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently in many optimization applications when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods can result in misleading outcomes because of model misspecification. In this paper, we consider nonsparse learning under the factors plus sparsity structure, which yields a joint modeling of sparse individual effects and common latent factors. A new methodology of nonsparse learning with latent variables (NSL) is proposed for joint estimation of the effects of two groups of features, one for individual effects and the other associated with the latent substructures, when the nonsparse effects are captured by the leading population principal component score vectors. We derive the convergence rates of both sample principal components and their score vectors that hold for a wide class of distributions. With the properly estimated latent variables, properties including model selection consistency and oracle inequalities under various prediction and estimation losses are established. Our new methodology and results are evidenced by simulation and real-data examples.

Keywords: high dimensionality; nonsparse coefficient vectors; factors plus sparsity structure; principal component analysis; spiked covariance; model selection (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://doi.org/10.1287/opre.2020.2005 (application/pdf)

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:inm:oropre:v:69:y:2021:i:1:p:346-359

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().