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

Zboňáková, L; Monti, RP; Härdle, WK; (2019) Towards the interpretation of time-varying regularization parameters in streaming penalized regression models. Pattern Recognition Letters , 125 pp. 542-548. 10.1016/j.patrec.2019.06.021. Green open access

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Abstract

High-dimensional, streaming datasets are ubiquitous in modern applications. Examples range from finance 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 misspecification. 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 financial data and another to neuroimaging data, where the aforementioned discussion is relevant.

Type: Article
Title: Towards the interpretation of time-varying regularization parameters in streaming penalized regression models
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.patrec.2019.06.021
Publisher version: https://doi.org/10.1016/j.patrec.2019.06.021
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit
URI: https://discovery.ucl.ac.uk/id/eprint/10086702
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