Abstract
Fitting models with high predictive accuracy that include all relevant but no irrelevant or redundant features is a challenging task on data sets with similar (e.g. highly correlated) features. We propose the approach of tuning the hyperparameters of a predictive model in a multi-criteria fashion with respect to predictive accuracy and feature selection stability. We evaluate this approach based on both simulated and real data sets and we compare it to the standard approach of single-criteria tuning of the hyperparameters as well as to the state-of-the-art technique “stability selection”. We conclude that our approach achieves the same or better predictive performance compared to the two established approaches. Considering the stability during tuning does not decrease the predictive accuracy of the resulting models. Our approach succeeds at selecting the relevant features while avoiding irrelevant or redundant features. The single-criteria approach fails at avoiding irrelevant or redundant features and the stability selection approach fails at selecting enough relevant features for achieving acceptable predictive accuracy. For our approach, for data sets with many similar features, the feature selection stability must be evaluated with an adjusted stability measure, that is, a measure that considers similarities between features. For data sets with only few similar features, an unadjusted stability measure suffices and is faster to compute.
The R source code for all analyses presented in this paper is publicly available at https://github.com/bommert/model-fitting-similar-features.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bommert, A.: Integration of Feature Selection Stability in Model Fitting. Ph.D. thesis, TU Dortmund University, Germany (2020)
Bommert, A., Rahnenführer, J.: Adjusted measures for feature selection stability for data sets with similar features. In: Nicosia, G., et al. (eds.) LOD 2020. LNCS, vol. 12565, pp. 203–214. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64583-0_19
Bommert, A., Rahnenführer, J., Lang, M.: A multicriteria approach to find predictive and sparse models with stable feature selection for high-dimensional data. Comput. Math. Methods Med. 2017, 7907163 (2017)
Brown, G., Pocock, A., Zhao, M.J., Luján, M.: Conditional likelihood maximisation: a unifying framework for information theoretic feature selection. J. Mach. Learn. Res. 13, 27–66 (2012)
Dash, M., Liu, H.: Feature selection for classification. Intell. Data Anal. 1, 131–156 (1997)
Hall, M.A.: Correlation-based feature selection for machine learning. Ph.D. thesis, University of Waikato, Hamilton, New Zealand (1999)
Hazimeh, H., Mazumder, R.: Fast best subset selection: coordinate descent and local combinatorial optimization algorithms. Oper. Res. Art. Adv. 68, 1526–5463 (2020)
Kalousis, A., Prados, J., Hilario, M.: Stability of feature selection algorithms: a study on high-dimensional spaces. Knowl. Inf. Syst. 12(1), 95–116 (2007)
Meinshausen, N., Bühlmann, P.: Stability selection. J. Roy. Stat. Soc. Ser. B (Stat. Methodol.) 72(4), 417–473 (2010)
Miettinen, K.: Introduction to multiobjective optimization: noninteractive approaches. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 1–26. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88908-3_1
Shah, R.D., Samworth, R.J.: Variable selection with error control: another look at stability selection. J. Roy. Stat. Soc. Ser. B (Stat. Methodol.) 75(1), 55–80 (2013)
Vanschoren, J., Van Rijn, J.N., Bischl, B., Torgo, L.: OpenML: networked science in machine learning. ACM SIGKDD Explor. Newsl. 15(2), 49–60 (2013)
Yu, L., Liu, H.: Efficient feature selection via analysis of relevance and redundancy. J. Mach. Learn. Res. 5, 1205–1224 (2004)
Acknowledgments
This work was supported by German Research Foundation (DFG), Project RA 870/7-1 and Collaborative Research Center SFB 876, A3. We acknowledge the computing time provided on the Linux HPC cluster at TU Dortmund University (LiDO3), partially funded in the course of the Large-Scale Equipment Initiative by the German Research Foundation (DFG) as Project 271512359.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Bommert, A., Rahnenführer, J., Lang, M. (2022). Employing an Adjusted Stability Measure for Multi-criteria Model Fitting on Data Sets with Similar Features. In: Nicosia, G., et al. Machine Learning, Optimization, and Data Science. LOD 2021. Lecture Notes in Computer Science(), vol 13163. Springer, Cham. https://doi.org/10.1007/978-3-030-95467-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-95467-3_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-95466-6
Online ISBN: 978-3-030-95467-3
eBook Packages: Computer ScienceComputer Science (R0)