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On Bayesian Network Classifiers with Reduced Precision Parameters

Published: 01 April 2015 Publication History

Abstract

Bayesian network classifier (BNCs) are typically implemented on nowadays desktop computers. However, many real world applications require classifier implementation on embedded or low power systems. Aspects for this purpose have not been studied rigorously. We partly close this gap by analyzing reduced precision implementations of BNCs. In detail, we investigate the quantization of the parameters of BNCs with discrete valued nodes including the implications on the classification rate (CR). We derive worst-case and probabilistic bounds on the CR for different bit-widths. These bounds are evaluated on several benchmark datasets. Furthermore, we compare the classification performance and the robustness of BNCs with generatively and discriminatively optimized parameters, i.e. parameters optimized for high data likelihood and parameters optimized for classification, with respect to parameter quantization. Generatively optimized parameters are more robust for very low bit-widths, i.e. less classifications change because of quantization. However, classification performance is better for discriminatively optimized parameters for all but very low bit-widths. Additionally, we perform analysis for margin-optimized tree augmented network (TAN) structures which outperform generatively optimized TAN structures in terms of CR and robustness.

References

[1]
S. Tschiatschek, P. Reinprecht, M. Mücke, and F. Pernkopf, “Bayesian network classifiers with reduced precision parameters,” in Proc. Eur. Conf. Mach. Learn. Knowl. Discov. Databases, 2012, pp. 74–89.
[2]
S. Tschiatschek, C. E. Cancino Chacón, and F. Pernkopf, “ Bounds for Bayesian network classifiers with reduced precision parameters,” in Proc. Int. Conf. Acoust., Speech, Signal Process., 2013, pp. 3357 –3361.
[3]
N. Friedman, D. Geiger, and M. Goldszmidt, “ Bayesian network classifiers,” Mach. Learn., vol. 29, pp. 131–163, 1997.
[4]
C. Bielza and P. Larrañaga, “Discrete Bayesian network classifiers: A survey,” ACM Comput. Surveys, vol. 47, no. 1, pp. 5:1–5:43, 2014.
[5]
F. Pernkopf, M. Wohlmayr, and S. Tschiatschek, “ Maximum margin Bayesian network classifiers,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 34, no. 3, pp. 521–531, Mar. 2012.
[6]
D. Husmeier, R. Dybowski, and S. Roberts, Probabilistic Modelling in Bioinformatics and Medical Informatics. New York, NY, USA: Springer, 2004.
[7]
P. Helman, R. Veroff, S. R. Atlas, and C. Willman, “A Bayesian network classification methodology for gene expression data,” Comput. Biol., vol. 11, pp. 581–615, 2004.
[8]
D.-U. Lee, A. Gaffar, R. C. C. Cheung, O. Mencer, W. Luk, and G. Constantinides, “Accuracy-guaranteed bit-width optimization,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 25, no. 10, pp. 1990–2000, Oct. 2006.
[9]
H. Chan and A. Darwiche, “When do numbers really matter?” Artif. Intell. Res., vol. 17, no. 1, pp. 265–287, 2002.
[10]
F. Pernkopf, M. Wohlmayr, and M. Mücke, “Maximum margin structure learning of Bayesian network classifiers,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2011, pp. 2076–2079.
[11]
S. Tschiatschek, K. Paul, and F. Pernkopf, “Integer Bayesian network classifiers,” in Proc. Eur. Conf. Mach. Learn. Knowl. Discov. Databases , 2014, pp. 209–224.
[12]
F. Pernkopf and J. Bilmes, “Efficient heuristics for discriminative structure learning of Bayesian network classifiers, ” J. Mach. Learn. Res., vol. 11, pp. 2323– 2360, Aug. 2010.
[13]
R. Peharz and F. Pernkopf, “Exact maximum margin structure learning of Bayesian networks,” in Proc. 29th Int. Conf. Mach. Learn., 2012.
[14]
R. Greiner and W. Zhou, “Structural extension to logistic regression: Discriminative parameter learning of belief net classifiers,” in Proc. Nat. Conf. Artif. Intell., 2002, pp. 167–173.
[15]
T. Roos, H. Wettig, P. Grünwald, P. Myllymäki, and H. Tirri, “On discriminative Bayesian network classifiers and logistic regression,” Mach. Learn., vol. 59, no. 3, pp. 267–296, 2005.
[16]
J. M. Bernardo and A. F. M. Smith, Bayesian Theory, New York, NY, USA: Wiley, 1994.
[17]
D. Heckerman, D. Geiger, and D. Chickering, “ Learning Bayesian networks: The combination of knowledge and statistical data,” Microsoft Res., Redmond, WA, USA, Tech. Rep. MSR-TR-91-05, 1995.
[18]
C. M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics) . New York, NY, USA: Springer, 2007.
[19]
J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference . San Francisco, CA, USA: Morgan Kaufmann, 1988.
[20]
D. Koller and N. Friedman, Probabilistic Graphical Models: Principles and Techniques. Cambridge, MA, USA : MIT Press, 2009.
[21]
I. Kononenko, “Semi-naive Bayesian classifier,” in Proc. Eur. Working Session Learn. Mach. Learn., 1991, pp. 206–219.
[22]
S. Acid, L. M. Campos, and J. G. Castellano, “ Learning Bayesian network classifiers: Searching in a space of partially directed acyclic graphs, ” Mach. Learn., vol. 59, pp. 213–235, 2005.
[23]
F. Pernkopf, R. Peharz, and S. Tschiatschek, “ Introduction to probabilistic graphical models,” in Academic Press Library in Signal Processing, vol. 1, 2014, ch. 18, pp. 989–1064.
[24]
Y. Guo, D. Wilkinson, and D. Schuurmans, “Maximum margin Bayesian networks,” in Proc. Uncertainty Artif. Intell., 2005, pp. 233–242.
[25]
N. Piatkowski, L. Sangkyun, and K. Morik, “The integer approximation of undirected graphical models,” in Proc. Int. Conf. Pattern Recognit. Appl. Methods, 2014, pp. 296–304.
[26]
B. Widrow, I. Kollar, and M. Liu, “Statistical theory of quantization,” IEEE Trans. Instrum. Meas., vol. 45, no. 2, pp. 353–361, Apr. 1996.
[27]
A. Papoulis, Probability, Random Variables, and Stochastic Processes. New York, NY, USA: McGraw-Hill, 1984.
[28]
T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction. New York, NY, USA : Springer, Aug. 2003.
[29]
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE, vol. 86, no. 11, pp. 2278–2324, Nov. 1998.
[30]
F. Pernkopf and M. Wohlmayr, “Stochastic margin-based structure learning of Bayesian network classifiers, ” Pattern Recognit., vol. 46, no. 2, pp. 464 –471, 2013.

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          Published In

          cover image IEEE Transactions on Pattern Analysis and Machine Intelligence
          IEEE Transactions on Pattern Analysis and Machine Intelligence  Volume 37, Issue 4
          April 2015
          208 pages

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          IEEE Computer Society

          United States

          Publication History

          Published: 01 April 2015

          Author Tags

          1. discriminative learning
          2. Bayesian network classifiers
          3. custom precision
          4. quantization

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          • (2021)Basketball sports neural network model based on nonlinear classificationJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-18943140:4(5917-5926)Online publication date: 1-Jan-2021
          • (2021)RETRACTED ARTICLE: Intelligent recommendation method integrating knowledge graph and Bayesian networkSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-021-05735-z27:1(483-492)Online publication date: 25-Mar-2021
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          • (2015)Rebooting Computing: New Strategies for Technology ScalingComputer10.1109/MC.2015.36348:12(10-13)Online publication date: 1-Dec-2015

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