یادگیری پارامترهای شبکه بیزی از داده حاوی مقادیر گم‌شده
الموضوعات :
کبری اطمینانی
1
(دانشگاه فردوسی مشهد)
محمود نقیب‌زاده
2
(دانشگاه فردوسی مشهد)
مهدی عمادی
3
(دانشگاه فردوسی مشهد)
امیررضا رضوی
4
(دانشگاه علوم پزشکی مشهد)
الکلمات المفتاحية: پارامترهای شبکه بیزی راست‌نمایی شبکه بیزی مقدار گم‌شده,
ملخص المقالة :
یادگیری ساختار شبکه بیزی از داده، در سال‌های اخیر توجه بسیاری از محققین را به خود جلب نموده است. از طرفی، یافتن شبکه بهینه از داده کامل، خود یک مسأله غیر چندجمله‌ای سخت می‌باشد و پیچیدگی مسأله، زمانی که داده ناقص است، بیشتر می‌شود. به طور کلی دو حالت یادگیری شبکه بیزی از داده ناقص وجود دارد: زمانی که ساختار مشخص است و زمانی که ساختار نیز نامشخص است. در این مقاله سعی بر آن است تا پارامترهای بهینه را برای یک شبکه بیزی با ساختار مشخص از داده حاوی مقادیر گم‌شده بیابیم. برای این منظور مفهوم "پارامتر مؤثر" را معرفی نمودیم، به طوری که درست‌نمایی ساختار شبکه به شرط داده کامل‌شده، بیشینه گردد. این روش می‌تواند به هر الگوریتمی همچون بیشینه‌سازی امید ساختاری که به پارامترهای بهینه برای یافتن ساختار شبکه بیزی نیاز دارند، متصل شود. در این مقاله ثابت کردیم که روش پیشنهادی از دیدگاه تابع درست‌نمایی به پارامترهای بهینه شبکه دست می‌یابد. نتایج اعمال روش پیشنهادی به چندین شبکه بیزی استاندارد، نشان‌دهنده سرعت روش در مقایسه با روش‌های شناخته‌شده قبلی است و نیز این که به پارامترهای بهتری نسبت به آنها دست می‌یابد.
[1] N. Friedman, M. Linial, I. Nachman, and D. Peer, "Using Bayesian networks to analyze expression data," Computational Biology, vol. 7, no. 3-4, pp. 601-620, 2000.
[2] J. Uebersax, Breast Cancer Risk Modeling: An Application of Bayes Networks, Technical Report, Ravenpack International, Spain, 2004.
[3] L. M. de Campos, J. M. Fernandez - Luna, and J. F. Huete, "Bayesian networks and information retrieval: an introduction to the special issue," Information Processing and Management, vol. 40, no. 5, pp. 727-733, Sep. 2004.
[4] F. J. Diez, J. Mira, E. Iturralde, S. Zubillaga, and A. Diaval, "A Bayesian expert system for echocardiography," Artificial Intelligence in Medicine, vol. 10, no. 1, pp. 59-73, May 1997.
[5] D. M. Chickering, "Learning bayesian network is NP - complete," Learning from Data: Artificial Intelligence and Statistics V, pp. 121-130, 1996.
[6] D. M. Chickering, C. Meek, and D. Heckerman, "Large-sample learning of Bayesian networks is NP-Hard," in Proc. 19th Conf. on Uncertainty in Artificial Intelligence, UAI'03, pp. 124-133, 2003.
[7] Z. Kebaili and A. Aussem, "A novel hybrid Bayesian network structure learning algorithm based on correlated itemset mining techniques," Int. J. of Computational Intelligence Research, vol. 5, no. 1, pp. 16-21, 2009.
[8] I. Tsamardinos, L. E. Brown, and C. F. Aliferis, "The max - min hill - climbing Bayesian network structure learning algorithm," Machine Learning, vol. 65, no. 1, pp. 31-78, 2006.
[9] D. Rubin, "Inference and missing data," Biometrika, vol. 63, no. 3, pp. 581-592, 1976.
[10] R. Little and D. Rubin, Statistical Analysis with Missing Data, Wiley - Interscience, 2002.
[11] G. Elidan, I. Nachman, and N. Friedman, "Ideal parent structure learning for continuous variable Bayesian networks," J. of Machine Learning Research, vol. 8, pp. 1799-1833, 2007.
[12] W. Buntine, "Theory refinement on Bayesian networks," in Proc. 7th Conf. on Uncertainty in Artificial Intelligence, UAI'91, pp. 52-60, 1991.
[13] T. Silander and P. Myllymaki, "A simple approach for finding the globally optimal Bayesian network structure," in Proc. 22nd Conf. on Uncertainty in Artificial Intelligence, UAI'06, pp. 445-452, 2006.
[14] A. P. Singh and A. W. Moore, Finding Optimal Bayesian Networks by Dynamic Programming, Technical Report, Carnegie Mellon University CALD-05-106, 2005.
[15] M. Koivisto and K. Sood, "Exact bayesian structure discovery in bayesian networks," J. of Machine Learning Research, vol. 5, pp. 549-573, 2004.
[16] J. Suzuki, "Learning Bayesian belief networks based on the minimum description length principle: an efficient algorithm using the branch and bound technique," IEICE Trans. Inf. & Syst., vol. E82-D, no. 2, pp. 356-367, Feb. 1999.
[17] C. P. de Campos, Z. Zeng, and Q. Ji, "Structure learning of Bayesian networks using constraints," in Proc. 26th Int. Conf. on Machine Learning, ICML'09, 2009.
[18] K. Etminani, M. Naghibzadeh, and A. R. Razavi, "Globally optimal structure learning of bayesian networks from data," Lecture Notes in Computer Science, vol. 6352, pp. 101-106, 2010.
[19] D. M. Chickering and D. Heckerman, "Efficient approximations for the marginal likelihood of bayesian networks with hidden variables," Machine Learning, vol. 29, no. 2-3, pp. 181-212, 1997.
[20] M. Ramoni and P. Sebastiani, "Learning Bayesian networks from incomplete databases," in Proc. of the Conf. on Uncertainty in AI, pp. 401-408, 1997.
[21] N. Friedman, "Learning belief network in the presence of missing values and hidden variables," in Proc.14th Int. Conf. on Machine Learning, pp. 125-133, 1997.
[22] N. Friedman, "The bayesian structural EM algorithm," in Proc. 14th Conf. on Uncertainty in Artificial Intelligence, 1998.
[23] A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. of the Royal Statistical Society B, vol. 39, no. 1, pp. 1-39, 1977.
[24] P. Leray and O. Franois, "Bayesian network structural learning and incomplete data," in Proc. Int. and Interdisciplinary Conf. on Adaptive Knowledge Representation and Reasoning, 2005.
[25] N. Friedman and M. Goldszmidt, "Discretizing continuous attributes while learning bayesian networks," in Proc. 13th Int. Conf. on Machine Learning, ICML'96, pp. 157-165, 1996.
[26] G. Cooper and E. Herskovits, "A bayesian method for the induction of probabilistic networks from data," Machine Learning, vol. 9, no. 4, pp. 309-347, 1992.
[27] D. Heckerman, D. Geiger, and D. M. Chickering, "Learning bayesian networks: the combination of knowledge and statistical data," Machine Learning, vol. 20, no. 3, pp. 197-243, 1995.
[28] G. Schwartz, "Estimating the dimensions of a model," Annals of Statistics, vol. 6, no. 2, pp. 461-464, 1978.
[29] J. Rissanen, "Stochastic complexity (with discussion)," J. of the Royal Statistical Society, vol. 49, no. 3, pp. 223-239, 1987.
[30] H. Akaike, "A new look at the statistical model identification," IEEE Trans. on Automatic Control, vol. 19, no. 6, pp. 716-723, 1974.
[31] S. L. Lauritzen and D. J. Spiegelhalter, "Local computations with probabilitieson graphical structures and their application to expert systems," J. of Royal Statistics Society, vol. 50, no. 2, pp. 157-224, 1988.
[32] R. E. Neapolitan, Probabilistic Reasoning in Expert Systems: Theory and Algorithms, John Wiley & Sons, Inc., pp. 179-180, 1990.
