High-dimensional regression in practice: an empirical study of finite-sample prediction, variable selection and ranking
Publication Date
2019-12-19Journal Title
Statistics and Computing
ISSN
0960-3174
Publisher
Springer US
Volume
30
Issue
3
Pages
697-719
Language
en
Type
Article
This Version
VoR
Metadata
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Wang, F., Mukherjee, S., Richardson, S., & Hill, S. M. (2019). High-dimensional regression in practice: an empirical study of finite-sample prediction, variable selection and ranking. Statistics and Computing, 30 (3), 697-719. https://doi.org/10.1007/s11222-019-09914-9
Abstract
Abstract: Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well developed, the relative efficacy of different approaches in finite-sample settings, as encountered in practice, remains incompletely understood. There is therefore a need for empirical investigations in this area that can offer practical insight and guidance to users. In this paper, we present a large-scale comparison of penalized regression methods. We distinguish between three related goals: prediction, variable selection and variable ranking. Our results span more than 2300 data-generating scenarios, including both synthetic and semisynthetic data (real covariates and simulated responses), allowing us to systematically consider the influence of various factors (sample size, dimensionality, sparsity, signal strength and multicollinearity). We consider several widely used approaches (Lasso, Adaptive Lasso, Elastic Net, Ridge Regression, SCAD, the Dantzig Selector and Stability Selection). We find considerable variation in performance between methods. Our results support a “no panacea” view, with no unambiguous winner across all scenarios or goals, even in this restricted setting where all data align well with the assumptions underlying the methods. The study allows us to make some recommendations as to which approaches may be most (or least) suitable given the goal and some data characteristics. Our empirical results complement existing theory and provide a resource to compare methods across a range of scenarios and metrics.
Keywords
Article, Simulation study, High-dimensional regression, Penalized regression, Lasso, Variable selection, Prediction
Sponsorship
Medical Research Council (MC_UU_00002/2, MC_UU_00002/10)
Identifiers
s11222-019-09914-9, 9914
External DOI: https://doi.org/10.1007/s11222-019-09914-9
This record's URL: https://www.repository.cam.ac.uk/handle/1810/315455
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/