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Semi-supervised weighting for averaged one-dependence estimators

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Abstract

Averaged one-dependence estimators (AODE) is a state-of-the-art machine learning tool for classification due to its simplicity, high computational efficiency, and excellent classification accuracy. Weighting provides an effective mechanism to ensemble superparent one-dependence estimators (SPODEs) in AODE by linearly aggregating their weighted probability estimates. Supervised weighting and unsupervised weighting are proposed to learn weights from labeled or unlabeled data, whereas their interoperability has not previously been investigated. In this paper, we propose a novel weighting paradigm in the framework of semi-supervised learning, called semi-supervised weighting (SSW). Two different versions of weighted AODEs, supervised weighted AODE (SWAODE) which performs weighting at training time and unsupervised weighted AODE (UWAODE) which performs weighting at classification time, are built severally. Log likelihood function is introduced to linearly aggregate the outcomes of these two weighted AODEs. The proposed algorithm, called SSWAODE, is validated on 38 benchmark datasets from the University of California at Irvine (UCI) machine learning repository and the experimental results prove the effectiveness and robustness of SSW for weighting AODE in terms of zero-one loss, bias, variance and etc. SSWAODE well achieves the balance between the ground-truth dependencies approximation and the effectiveness of probability estimation.

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References

  1. Heckerman D, Geiger D, Chickering DM (1995) Learning Bayesian networks: the combination of knowledge and statistical data. Mach Learn 20:197–243

    MATH  Google Scholar 

  2. Duan ZY, Wang LM, Sun MH (2020) Efficient heuristics for learning Bayesian network from labeled and unlabeled data. Intell Data Anal 24(2):385–408

    Article  Google Scholar 

  3. Jiang LX, Zhang LG, Yu LJ, Wang DH (2019) Class-specific attribute weighted naive Bayes. Pattern Recogn 88:321–330

    Article  Google Scholar 

  4. Friedman N, Geiger D, Goldszmidt M (1997) Bayesian network classifiers. Mach Learn 29(2&3):131–163

    Article  Google Scholar 

  5. Zhang XL, Li XF, Feng YC (2016) A classification performance measure considering the degree of classification difficulty. Neurocomputing 193:81–91

    Article  Google Scholar 

  6. Wang LM, Chen P, Chen SL, Sun MH (2021) A novel approach to fully representing the diversity in conditional dependencies for learning Bayesian network classifier. Intell Data Anal 25(1):35–55

    Article  Google Scholar 

  7. Liu Y, Wang LM, Mammadov M, Chen SL, Wang GJ, Qi SK, Sun MH (2021) Hierarchical independence thresholding for learning Bayesian network classifiers. Knowl-based Syst 212:106627

    Article  Google Scholar 

  8. Pang SC, Yu ZZ, Orgun MA (2017) A novel end-to-end classifier using domain transferred deep convolutional neural networks for biomedical images. Comput Methods Programs Biomed 140:283–293

    Article  Google Scholar 

  9. Wang LM, Qi SK, Liu Y, Lou H, Zuo X (2021) Bagging k-dependence Bayesian network classifiers. Intell Data Anal 25(3):641–667

    Article  Google Scholar 

  10. Webb GI, Boughton JR, Wang ZH (2005) Not so naive Bayes: Aggregating One-Dependence Estimators. Mach Learn 58(1):5–24

    Article  Google Scholar 

  11. Liu Y, Wang LM, Mammadov M (2020) Learning semi-lazy Bayesian network classifier under the c.i.i.d assumption. Knowledge-based Systems 208:106422

    Article  Google Scholar 

  12. Zaidi NA, Webb GI (2013) Fast and effective single pass Bayesian learning. In: Advances in knowledge discovery and data mining, pp 149–160

  13. Kong H, Shi XH, Wang LM, Liu Y, Mammadov M, Wang GJ (2021) Averaged tree-augmented one-dependence estimators. Appl Intell 51:4270–4286

    Article  Google Scholar 

  14. Yang Y, Webb GI, Cerquides J, Korb K, Boughton J, Ting KM (2007) To select or to weigh: A comparative study of linear combination schemes for superparent-one-dependence estimators. IEEE Trans Knowl Data Eng 19(12):1652–1665

    Article  Google Scholar 

  15. Jiang LX, Zhang H, Cai ZH, Wang DH (2012) Weighted average of one-dependence estimators. J Exper Theor Artif Intell 24(2):219–230

    Article  Google Scholar 

  16. Xiang ZL, Kang DK (2016) Attribute weighting for averaged one-dependence estimators. Appl Intell 46(3):616–629

    Article  Google Scholar 

  17. Yu LJ, Jiang LX, Wang DH, Zhang LG (2017) Attribute value weighted average of one-dependence estimators. Entropy 19(9):501

    Article  Google Scholar 

  18. Wang LM, Chen J, Liu Y, Sun MH (2020) Self-adaptive attribute value weighting for averaged one-dependence estimators. IEEE Access 8:27887–27900

    Article  Google Scholar 

  19. Duan ZY, Wang LM, Chen SL, Sun MH (2020) Instance-based weighting filter for superparent one-dependence estimators. Knowl-based Syst 203:106085

    Article  Google Scholar 

  20. Chen SL, Martínez AM, Webb GI, Wang LM (2017) Sample-based attribute selective An DE for large data. IEEE Trans Knowl Data Eng 29(1):172–185

    Article  Google Scholar 

  21. Yang Y, Korb K, Ting KM, Webb GI (2005) Ensemble selection for superparent-one-dependence estimators. In: Proceedings of the 18th Australian joint conference on artificial intelligence, pp 102–112

  22. Han M, Ding J (2012) Selection for superparent one dependence estimators based on MDL. In: Proceedings of international conference on artificial intelligence and computational intelligence. pp 166–173

  23. Chen SL, Martínez AM, Webb GI, Wang LM (2017) Selective An DE for large data learning: a low-bias memory constrained approach. Knowl Inf Syst 50(2):475–503

    Article  Google Scholar 

  24. Jiang LX, Zhang H (2006) Lazy averaged one-dependence estimators. In: Proceedings of the 19th conference of the canadian-society-for-computational-studies-of-intelligence, pp 515–525

  25. Zheng F, Webb GI (2006) Efficient lazy elimination for averaged one-dependence estimators. In: Proceedings of the 23rd international conference on machine learning, pp 1113–1120

  26. Murphy PM, Aha DW (2021) UCI repository of machine learning databases. Available online: http://www.ics.uci.edu/mlearn/MLRepository.html

  27. Cestnik B (1990) Estimating probabilities: a crucial task in machine learning. In: Proceedings of the 9th European conference on artificial intelligence, pp 147–149

  28. Toshitaka H, Hamido F, Andres H (2021) Less complexity one-class classification approach using construction error of convolutional image transformation network. Inform Sci 560:217–234

    Article  MathSciNet  Google Scholar 

  29. Chichering DM, Heckerman D, Meek C (2004) Large-sample learning of Bayesian networks is NP-hard. J Mach Learn Res 5:1287–1330

    MathSciNet  MATH  Google Scholar 

  30. Langley P, Iba W, Thompson K (1992) An analysis of Bayesian classifiers. In: Proceedings of american association for artificial intelligence, pp 223–228

  31. Jiang LX, Zhang LG, Li CQ, Wu J (2019) A correlation-based feature weighting filter for naive Bayes. IEEE Trans Knowl Data Eng 31(2):201–213

    Article  Google Scholar 

  32. Zaidi NA, Cerquides J, Carman MJ, Webb GI (2013) Alleviating naive bayes attribute independence assumption by attribute weighting. J Mach Learn Res 14:1947–1988

    MathSciNet  MATH  Google Scholar 

  33. Jiang LX, Cai ZH, Wang DH, Zhang H (2012) Improving Tree augmented Naive Bayes for class probability estimation. Knowl-based Syst 26:239–245

    Article  Google Scholar 

  34. Zheng F, Webb GI, Suraweera P, Zhu LG (2012) Subsumption resolution: an efficient and effective technique for semi-naive Bayesian learning. Mach Learn 87(1):93–125

    Article  MathSciNet  Google Scholar 

  35. Breiman L (1996) Bagging predictors. Mach Learn 24:123–140

    MATH  Google Scholar 

  36. Fayyad U, Irani K (1993) Multi-interval discretization of continuous-valued attributes for classification learning. In: Proceedings of the 13th international joint conferences on artificial intelligence, pp 1022–1029

  37. Kohavi R, Wolpert DH (1996) Bias plus variance decomposition for zero one loss functions. In: Proceedings of the 13th international conference, pp 275–283

  38. Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143(1):29–36

    Article  Google Scholar 

  39. Friedman M (1940) A comparison of alternative tests of significance for the problem of m rankings. Ann Math Stats 11(1):86–92

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank the editor and the anonymous reviewers for their insightful comments and suggestions. And this work was supported by the National Key Research and Development Program of China (No. 2019YFC1804804) and the Scientific and Technological Developing Scheme of Jilin Province (No. 20200201281JC).

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Authors and Affiliations

  1. Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, ChangChun, 130012, China

    Limin Wang

  2. College of Computer Science and Technology, Jilin University, ChangChun, 130012, China

    Shuai Zhang, Kuo Li & Siyuan Wu

  3. School of Information Technology, Deakin University, Victoria, 3125, Australia

    Musa Mammadov

  4. College of Mathematics, Jilin University, Changchun, 130012, China

    Xinhao Zhang

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  1. Limin Wang
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  2. Shuai Zhang
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  4. Kuo Li
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  5. Xinhao Zhang
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  6. Siyuan Wu
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Correspondence to Limin Wang.

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Wang, L., Zhang, S., Mammadov, M. et al. Semi-supervised weighting for averaged one-dependence estimators. Appl Intell 52, 4057–4073 (2022). https://doi.org/10.1007/s10489-021-02650-6

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