Skip to main content
Log in

On selective learning in stochastic stepwise ensembles

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Ensemble learning has attracted much attention of researchers studying variable selection due to its great power in improving selection accuracy and stabilizing selection results. In this paper, we present a novel ensemble pruning technique called Pruned-ST2E to obtain more effective variable selection ensembles. The order to aggregate the individuals generated by the ST2E algorithm (Xin and Zhu in J Comput Graph Stat 21(2):275–294, 2012) is rearranged. To estimate the importance of each candidate variable, only some members ranked ahead are remained. Experiments with simulated and real-world data show that the performance of Pruned-ST2E is comparable or superior to several other benchmark methods. Through analyzing the accuracy–diversity pattern in both ST2E and Pruned-ST2E, it is revealed that the inserted pruning step excludes less accurate members. The reserved members also become more concentrated on the true importance vector. Moreover, Pruned-ST2E is easy to implement. Therefore, Pruned-ST2E can be considered as an alternative for tackling variable selection tasks in practice.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Breiman L (1996) Heuristics of instability and stabilization in model selection. Ann Stat 24(6):2350–2383

    Article  MathSciNet  Google Scholar 

  2. Cai J, Luo JW, Wang SL, Yang S (2018) Feature selection in machine learning: a new perspective. Neurocomputing 300:70–79

    Article  Google Scholar 

  3. Che JL, Yang YL (2017) Stochastic correlation coefficient ensembles for variable selection. J Appl Stat 44(10):1721–1742

    Article  MathSciNet  Google Scholar 

  4. Che JL, Yang YL, Li L, Bai XY, Zhang SH, Deng CZ (2017) Maximum relevance minimum common redundancy feature selection for nonlinear data. Inf Sci 409–410:68–86

    Article  Google Scholar 

  5. Chung D, Kim H (2015) Accurate ensemble pruning with PL-bagging. Comput Stat Data Anal 83:1–13

    Article  MathSciNet  Google Scholar 

  6. Efron B, Hastie T, Hohnstone I, Tibshirani R (2004) Least angle regression. Ann Stat 32(2):407–499

    Article  MathSciNet  Google Scholar 

  7. Fan JQ, Li RZ (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96(456):1348–1360

    Article  MathSciNet  Google Scholar 

  8. Fan JQ, Lv JC (2008) Sure independence screening for ultrahigh dimensional feature space (with discussions). J R Stat Soc (Ser B) 70(5):849–911

    Article  MathSciNet  Google Scholar 

  9. Fan JQ, Lv JC (2010) A selective overview of variable selection in high dimensional feature space. Stat Sin 20(1):101–148

    MathSciNet  MATH  Google Scholar 

  10. Fakhraei S, Soltanian-Zadeh H, Fotouhi F (2014) Bias and stability of single variable classifiers for feature ranking and selection. Exp Syst Appl 41(15):6945–6958

    Article  Google Scholar 

  11. Genuer R, Poggi JM, Tuleau-Malot C (2010) Variable selection using random forests. Pattern Rocognit Lett 31(14):2225–2236

    Article  Google Scholar 

  12. Griffin J, Brown P (2017) Hierarchical shrinkage priors for regression models. Bayes Anal 12(1):135–159

    Article  MathSciNet  Google Scholar 

  13. Kuncheva LI (2014) Combining pattern classifiers: methods and algorithms, 2nd edn. Wiley, Hoboken

    MATH  Google Scholar 

  14. Dua D, Graff C (2019) UCI machine learning repository. http://archive.ics.uci.edu/ml. Accessed Dec 2016

  15. Martínez-Muñoz G, Suárez A (2007) Using boosting to prune boosting ensembles. Pattern Recognit Lett 28(1):156–165

    Article  Google Scholar 

  16. Martínez-Muñoz G, Hernández-Lobato D, Suárez A (2009) An analysis of ensemble pruning techniues based on ordered aggregation. IEEE Trans Pattern Anal Mach Intell 31(2):245–259

    Article  Google Scholar 

  17. Meinshausen N, Bühlmann P (2010) Stability selection (with discussion). J R Stat Soc B 72(4):417–473

    Article  MathSciNet  Google Scholar 

  18. Mendes-Moreira J, Soares C, Jorge AM, de Sousa JF (2012) Ensemble approaches for regression: a survey. ACM Comput Surv 45(1):40 Article 10

    Article  Google Scholar 

  19. Miller A (2002) Subset selection in regression, 2nd edn. Chapman & Hall/CRC Press, New Work

    Book  Google Scholar 

  20. Nan Y, Yang YH (2014) Variable selection diagnostics measures for high-dimensional regression. J Comput Graph Stat 23(3):636–656

    Article  MathSciNet  Google Scholar 

  21. Peng HC, Long FH, Ding C (2005) Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans Pattern Anal Mach Intel 27(8):1226–1238

    Article  Google Scholar 

  22. Rokach L (2016) Decision forest: twenty years of research. Inf Fus 27:111–125

    Article  Google Scholar 

  23. Sauerbrei W, Buchholz A, Boulesteix AL, Binder H (2015) On stability issues in deriving multivariable regression models. Biometrical J 57(4):531–555

    Article  MathSciNet  Google Scholar 

  24. Subrahmanya N, Shin YC (2013) A variational Bayesian framework for group feature selection. Intern J Mach Learn Cybern 4(6):609–619

    Article  Google Scholar 

  25. Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc B 58(1):267–288

    MathSciNet  MATH  Google Scholar 

  26. Tibshirani R, Walther G, Hastie T (2001) Estimating the number of clusters in a data set via the gap statistic. J R Stat Soc (Ser B) 63(2):411–423

    Article  MathSciNet  Google Scholar 

  27. Wang SJ, Nan B, Rosset S, Zhu J (2011) Random lasso. Ann Appl Stat 5(1):468–485

    Article  MathSciNet  Google Scholar 

  28. Xin L, Zhu M (2012) Stochastic stepwise ensembles for variable selection. J Comput Graph Stat 21(2):275–294

    Article  MathSciNet  Google Scholar 

  29. Zhang CX, Wang GW, Liu JM (2015) RandGA: injecting randomness into parallel genetic algorithm for variable selection. J Appl Stat 42(3):630–647

    Article  MathSciNet  Google Scholar 

  30. Zhang CX, Zhang JS, Kim SW (2016a) PBoostGA: pseudo-boosting genetic algorithm for variable ranking and selection. Comput Stat 31(4):1237–1262

    Article  MathSciNet  Google Scholar 

  31. Zhang CX, Ji NN, Wang GW (2016b) Randomizing outputs to increase variable selection accuracy. Neurocomputing 218:91–102

    Article  Google Scholar 

  32. Zhang CX, Zhang JS, Yin QY (2017) A ranking-based strategy to prune variable selection ensembles. Knowl Based Syst 125:13–25

    Article  Google Scholar 

  33. Zhou ZH, Wu JX, Tang W (2002) Ensembling neural networks: many could be better than all. Artif Intel 137(1–2):239–263

    Article  MathSciNet  Google Scholar 

  34. Zhu M, Chipman HA (2006) Darwinian evolution in parallel universes: a parallel genetic algorithm for variable selection. Technometrics 48(4):491–502

    Article  MathSciNet  Google Scholar 

  35. Zhu M, Fan GZ (2011) Variable selection by ensembles for the Cox model. J Stat Comput Simul 81(12):1983–1992

    Article  MathSciNet  Google Scholar 

  36. Zou H (2006) The adaptive lasso and its oracle properties. J Am Stat Assoc 101(476):1418–1429

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editor and reviewers for their useful comments which helped to improve the paper. This research was supported by the National Natural Science Foundation of China (Nos. 11671317, 61572393) and the National Research Foundation of Korea (No. NRF-2012R1A1A2041661).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chun-Xia Zhang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, CX., Kim, SW. & Zhang, JS. On selective learning in stochastic stepwise ensembles. Int. J. Mach. Learn. & Cyber. 11, 217–230 (2020). https://doi.org/10.1007/s13042-019-00968-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-019-00968-9

Keywords

Navigation