Towards the interpretation of time-varying regularization parameters in streaming penalized regression models

Lenka Zbonakova, Ricardo Pio Monti and Wolfgang Härdle

No 2018-059, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: High-dimensional, streaming datasets are ubiquitous in modern applications. Examples range from nance and e-commerce to the study of biomedical and neuroimaging data. As a result, many novel algorithms have been proposed to address challenges posed by such datasets. In this work, we focus on the use of L1 regularized linear models in the context of (possibly non-stationary) streaming data. Recently, it has been noted that the choice of the regularization parameter is fundamental in such models and several methods have been proposed which iteratively tune such a parameter in a time-varying manner, thereby allowing the underlying sparsity of estimated models to vary. Moreover, in many applications, inference on the regularization parameter may itself be of interest, as such a parameter is related to the underlying sparsity of the model. However, in this work, we highlight and provide extensive empirical evidence regarding how various (often unrelated) statistical properties in the data can lead to changes in the regularization parameter. In particular, through various synthetic experiments, we demonstrate that changes in the regularization parameter may be driven by changes in the true underlying sparsity, signal-to-noise ratio or even model misspecication. The purpose of this letter is, therefore, to highlight and catalog various statistical properties which induce changes in the associated regularization parameter. We conclude by presenting two applications: one relating to nancial data and another to neuroimaging data, where the aforementioned discussion is relevant.

Keywords: Lasso; penalty parameter; stock prices; neuroimaging (search for similar items in EconPapers)
JEL-codes: C13 C15 C63 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/230770/1/irtg1792dp2018-059.pdf (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:zbw:irtgdp:2018059

Access Statistics for this paper

More papers in IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series" Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().