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Probability Quantization Model for Sample-to-Sample Stochastic Sampling

  • Research Article-Computer Engineering and Computer Science
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Abstract

Computer-driven sampling methodology has been widely used in various application scenarios, theoretical models and data preprocessing. However, these powerful models are either based on explicit probability models or adopt data-level generation rules, which are difficult to be applied to the realistic environment that the prior distribution knowledge is missing. Inspired by the density estimation methods and quantization techniques, a method based on the quantization modeling of data density named probability quantization model (PQM) is proposed in this paper. The method quantifies the complex density estimation model through the discrete probability blocks so as to approximate the cumulative distribution and finally achieve backtracking sampling based on the roulette wheel selection and local linear regression, which avoids the indispensable prior distribution knowledge and troublesome modeling constraints in the existing stochastic sampling methods. Meanwhile, our method based on the data probability modeling is hard to be influenced by the sample features, thus avoiding over-fitting and having better data diversity than over-sampling methods. Experimental results show the advantages of the proposed method to various computer-driven sampling methods in terms of accuracy, generalization performance and data diversity.

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References

  1. Wang, Z.; Liu, L.; Li, K.: Dynamic Markov chain Monte Carlo-based spectrum sensing. IEEE Signal Process. Lett. 27, 1380–1384 (2020). https://doi.org/10.1109/LSP.2020.3013529

    Article  Google Scholar 

  2. Martino, L.; Luengo, D.: Extremely efficient acceptance-rejection method for simulating uncorrelated Nakagami fading channels. Commun. Stat. Simul. Comput. 48, 1798–1814 (2019). https://doi.org/10.1080/03610918.2018.1423694

    Article  MathSciNet  MATH  Google Scholar 

  3. Liu, Y.; Xiong, M.; Wu, C.; Wang, D.; Liu, Y.; Ding, J.; Huang, A.; Fu, X.; Qiang, X.; Xu, P.; Deng, M.; Yang, X.; Wu, J.: Sample caching Markov chain Monte Carlo approach to boson sampling simulation. New J. Phys. (2020). https://doi.org/10.1088/1367-2630/ab73c4

    Article  Google Scholar 

  4. Li, C.; Tian, Y.; Chen, X.; Li, J.: An efficient anti-quantum lattice-based blind signature for blockchain-enabled systems. Inf. Sci. (Ny) 546, 253–264 (2021)

    Article  MathSciNet  Google Scholar 

  5. Su, H.S.; Zhang, J.X.; Zeng, Z.G.: Formation-containment control of multi-robot systems under a stochastic sampling mechanism. Sci. China Technol. Sci. 63, 1025–1034 (2020). https://doi.org/10.1007/s11431-019-1451-6

    Article  Google Scholar 

  6. Li, M.; Dushoff, J.; Bolker, B.M.: Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches. Stat. Methods Med. Res. 27, 1956–1967 (2018). https://doi.org/10.1177/0962280217747054

    Article  MathSciNet  Google Scholar 

  7. Kim, M.; Lee, J.: Hamiltonian Markov chain Monte Carlo for partitioned sample spaces with application to Bayesian deep neural nets. J. Korean Stat. Soc. 49, 139–160 (2020). https://doi.org/10.1007/s42952-019-00001-3

    Article  MathSciNet  MATH  Google Scholar 

  8. Moka, S.B.; Kroese, D.P.: Perfect sampling for Gibbs point processes using partial rejection sampling. Bernoulli 26, 2082–2104 (2020)

    Article  MathSciNet  Google Scholar 

  9. Warne, D.J.; Baker, R.E.; Simpson, M.J.: Multilevel rejection sampling for approximate Bayesian computation. Comput. Stat. Data Anal. 124, 71–86 (2018)

    Article  MathSciNet  Google Scholar 

  10. Choe, Y.; Byon, E.; Chen, N.: Importance sampling for reliability evaluation with stochastic simulation models. Technometrics 57, 351–361 (2015)

    Article  MathSciNet  Google Scholar 

  11. Jiang, L.; Singh, S.S.: Tracking multiple moving objects in images using Markov Chain Monte Carlo. Stat. Comput. 28, 495–510 (2018). https://doi.org/10.1007/s11222-017-9743-9

    Article  MathSciNet  MATH  Google Scholar 

  12. Chan, T.C.Y.; Diamant, A.; Mahmood, R.: Sampling from the complement of a polyhedron: An MCMC algorithm for data augmentation. Oper. Res. Lett. 48, 744–751 (2020)

    Article  MathSciNet  Google Scholar 

  13. Yang, X.; Kuang, Q.; Zhang, W.; Zhang, G.: AMDO: An over-sampling technique for multi-class imbalanced problems. IEEE Trans. Knowl. Data Eng. 30, 1672–1685 (2018)

    Article  Google Scholar 

  14. Robert, C.P.; Casella, G.: Monte Carlo statistical methods. Springer(Chapter 2), New York (2004).

  15. Jia, G.; Taflanidis, A.A.; Beck, J.L.: A new adaptive rejection sampling method using kernel density approximations and its application to subset simulation. ASCE-ASME J. Risk Uncertain. Eng. Syst. Part A Civ. Eng. 3, 1–12 (2017). https://doi.org/10.1061/ajrua6.0000841

  16. Rao, V.; Lin, L.; Dunson, D.B.: Data augmentation for models based on rejection sampling. Biometrika 103, 319–335 (2016). https://doi.org/10.1093/biomet/asw005

    Article  MathSciNet  MATH  Google Scholar 

  17. Gilks, W.R.; Wild, P.: Adaptive rejection sampling for Gibbs sampling. Appl. Stat. 41, 337–348 (1992)

    Article  Google Scholar 

  18. Martino, L.: Parsimonious adaptive rejection sampling. Electron. Lett. 53, 1115–1117 (2017). https://doi.org/10.1049/el.2017.1711

    Article  Google Scholar 

  19. Martino, L.; Louzada, F.: Adaptive rejection sampling with fixed number of nodes. Commun. Stat. Simul. Comput. 48, 655–665 (2019). https://doi.org/10.1080/03610918.2017.1395039

    Article  MathSciNet  MATH  Google Scholar 

  20. Botts, C.: A modified adaptive accept-reject algorithm for univariate densities with bounded support. J. Stat. Comput. Simul. 81, 1039–1053 (2011)

    Article  MathSciNet  Google Scholar 

  21. Martino, L.: A review of multiple try MCMC algorithms for signal processing. Digit. Signal Process. A Rev. J. 75, 134–152 (2018). https://doi.org/10.1016/j.dsp.2018.01.004

    Article  MathSciNet  Google Scholar 

  22. Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109 (1970)

    Article  MathSciNet  Google Scholar 

  23. Mijatovic, A.; Vogrinc, J.: On the Poisson equation for Metropolis-Hastings chains. Bernoulli 24, 2401–2428 (2018). https://doi.org/10.3150/17-BEJ932

    Article  MathSciNet  MATH  Google Scholar 

  24. Li, H.; Li, J.; Chang, P.C.; Sun, J.: Parametric prediction on default risk of Chinese listed tourism companies by using random oversampling, isomap, and locally linear embeddings on imbalanced samples. Int. J. Hosp. Manag. 35, 141–151 (2013)

    Article  Google Scholar 

  25. Abu Alfeilat, H.A.; Hassanat, A.B.A.; Lasassmeh, O.; Tarawneh, A.S.; Alhasanat, M.B.; Eyal Salman, H.S.; Prasath, V.B.S.: Effects of distance measure choice on K-nearest neighbor classifier performance: a review. Big Data. 7, 221–248 (2019). https://doi.org/10.1089/big.2018.0175

    Article  Google Scholar 

  26. Chawla, N.V.; Bowyer, K.W.; Hall, L.O.; Kegelmeyer, W.P.: SMOTE: Synthetic minority over-sampling technique. J. Artif. Intell. Res. 16, 321–357 (2002)

    Article  Google Scholar 

  27. Xu, X.; Chen, W.; Sun, Y.: Over-sampling algorithm for imbalanced data classification. J. Syst. Eng. Electron. 30, 1182–1191 (2019). https://doi.org/10.21629/JSEE.2019.06.12

    Article  Google Scholar 

  28. Han, H.; Wang, W.Y.; Mao, B.H.: Borderline-SMOTE: A new over-sampling method in imbalanced data sets learning. In: Proc. Int. Conf. Intell. Comput. Berlin, Germany: Springer. pp. 878–887 (2005).

  29. He, H.B.; Yang, B.; Garcia, E.A.; Li, S.: ADASYN: adaptive synthetic sampling approach for imbalanced learning. In: Proc. of the IEEE World Congress on Computational Intelligence. pp. 1322–1328 (2008).

  30. Douzas, G.; Bacao, F.; Last, F.: Improving imbalanced learning through a heuristic oversampling method based on k-means and SMOTE. Inf. Sci. (Ny) 465, 1–20 (2018). https://doi.org/10.1016/j.ins.2018.06.056

    Article  Google Scholar 

  31. Tang, Y.; Zhang, Y.Q.; Chawla, N.V.; Krasser, S.: SVMs modeling for highly imbalanced classification. IEEE Trans. Syst. Man Cybern. B Cybern. 39, 281–288 (2009)

    Article  Google Scholar 

  32. Ahmed, H.I.; Wei, P.; Memon, I.; Du, Y.; Xie, W.: Estimation of time difference of arrival ( TDOA ) for the source radiates BPSK signal. IJCSI Int. J. Compuer Sci. 10, 164–171 (2013)

    Google Scholar 

  33. Yu, L.; Yang, T.; Chan, A.B.: Density-preserving hierarchical EM algorithm: simplifying Gaussian mixture models for approximate inference. IEEE Trans. Pattern Anal. Mach. Intell. 41, 1323–1337 (2019). https://doi.org/10.1109/TPAMI.2018.2845371

    Article  Google Scholar 

  34. Taaffe, K.; Pearce, B.; Ritchie, G.: Using kernel density estimation to model surgical procedure duration. Int. Trans. Oper. Res. 28, 401–418 (2021)

    Article  MathSciNet  Google Scholar 

  35. Cheng, M.; Hoang, N.D.: Slope collapse prediction using bayesian framework with K-nearest neighbor density estimation: case study in Taiwan. J. Comput. Civil Eng. 30, 04014116 (2016)

    Article  Google Scholar 

  36. Li, Y.; Zhang, Y.; Yu, M.; Li, X.: Drawing and studying on histogram. Cluster Comput. 22, S3999–S4006 (2019). https://doi.org/10.1007/s10586-018-2606-0

    Article  Google Scholar 

  37. Qin, H.; Gong, R.; Liu, X.; Bai, X.; Song, J.; Sebe, N.: Binary neural networks: A survey. Pattern Recognit. 105, 107281 (2020)

    Article  Google Scholar 

  38. Castillo-Barnes, D.; Martinez-Murcia, F.J.; Ramírez, J.; Górriz, J.M.; Salas-Gonzalez, D.: Expectation-Maximization algorithm for finite mixture of α-stable distributions. Neurocomputing 413, 210–216 (2020). https://doi.org/10.1016/j.neucom.2020.06.114

    Article  Google Scholar 

  39. Ho-Huu, V.; Nguyen-Thoi, T.; Truong-Khac, T.; Le-Anh, L.; Vo-Duy, T.: An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints. Neural Comput. Appl. 29, 167–185 (2018)

    Article  Google Scholar 

  40. Qian, W.; Chai, J.; Xu, Z.; Zhang, Z.: Differential evolution algorithm with multiple mutation strategies based on roulette wheel selection. Appl. Intell. 48, 3612–3629 (2018). https://doi.org/10.1007/s10489-018-1153-y

    Article  Google Scholar 

  41. Goodfellow, I.; Pouget-Abadie, J.; Mirza, M.; Xu, B.; Warde-Farley, D.; Ozair, S.; Courville, A.; Bengio, Y.: Generative Adversarial Nets. Advances in Neural Information Processing Systems, p. 2672–2680. Springer, Berlin (2014)

    Google Scholar 

  42. Ponti, M.; Kittler, J.; Riva, M.; de Campos, T.; Zor, C.: A decision cognizant Kullback-Leibler divergence. Pattern Recognit. 61, 470–478 (2017). https://doi.org/10.1016/j.patcog.2016.08.018

    Article  Google Scholar 

  43. Arain, Q.A.; Memon, H.; Memon, I.; Memon, M.H.; Shaikh, R.A.; Mangi, F.A.: Intelligent travel information platform based on location base services to predict user travel behavior from user-generated GPS traces. Int. J. Comput. Appl. 39, 155–168 (2017). https://doi.org/10.1080/1206212X.2017.1309222

    Article  Google Scholar 

  44. Chen, X.; Kar, S.; Ralescu, D.A.: Cross-entropy measure of uncertain variables. Inf. Sci. (Ny) 201, 53–60 (2012). https://doi.org/10.1016/j.ins.2012.02.049

    Article  MathSciNet  MATH  Google Scholar 

  45. Zhou, D.X.: Theory of deep convolutional neural networks: Downsampling. Neural Netw. 124, 319–327 (2020). https://doi.org/10.1016/j.neunet.2020.01.018

    Article  MATH  Google Scholar 

  46. Krizhevsky, A.; Sutskever, I.; Hinton, G.G.: Imagenet classification with deep convolutional neural networks. NIPS. 25, 1097–1105 (2012)

    Google Scholar 

  47. Yu, Y.; Si, X.; Hu, C.; Zhang, J.: A review of recurrent neural networks: LSTM cells and network architectures. NEURAL Comput. 31, 1235–1270 (2019). https://doi.org/10.1162/NECO

    Article  MathSciNet  MATH  Google Scholar 

  48. Scott, D.W.; Terrell, G.R.: Biased and unbiased cross-validation in density estimation. J. Am. Stat. Assoc. 82, 1131–1146 (1987)

    Article  MathSciNet  Google Scholar 

  49. Raykar, V.C.; Duraiswami, R.; Zhao, L.H.: Fast computation of kernel estimators. J. Comput. Graph. Stat. 19, 205–220 (2010)

    Article  MathSciNet  Google Scholar 

  50. Marron, J.S.; Wand, M.P.: Exact mean integrated squared error. Ann. Stat. 20, 712–736 (1992)

    Article  MathSciNet  Google Scholar 

  51. Wang, Z.; Huang, Y.; Lyu, S.X.: Lattice-reduction-aided Gibbs algorithm for lattice Gaussian sampling: Convergence Enhancement and Decoding Optimization. IEEE Trans. Signal Process. 67, 4342–4356 (2019)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank anonymous reviewers for their comments, which greatly helped improve the quality of the paper. This research has been supported by the Educational Commission of Guangdong Province, China (No.: 2020ZDZX3093).

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Authors and Affiliations

  1. Shenzhen Polytechnic, Shenzhen, 518055, China

    Bopeng Fang & Jing Wang

  2. Research Institute of New Energy Vehicle Technology, Shenzhen Polytechnic, Shenzhen, 518055, China

    Bopeng Fang, Zhurong Dong & Kai Xu

  3. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China

    Bopeng Fang

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  1. Bopeng Fang
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Correspondence to Zhurong Dong.

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Fang, B., Wang, J., Dong, Z. et al. Probability Quantization Model for Sample-to-Sample Stochastic Sampling. Arab J Sci Eng 47, 10865–10886 (2022). https://doi.org/10.1007/s13369-022-06932-0

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