Parameter learning in hybrid Bayesian networks using prior knowledge

详细信息    查看全文

• 作者：Inmaculada Pérez-Bernabé ; Antonio Fernández…
• 关键词：Hybrid Bayesian networks ; Mixtures of truncated basis functions ; Parameter learning ; Prior information
• 刊名：Data Mining and Knowledge Discovery
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：30
• 期：3
• 页码：576-604
• 全文大小：1,370 KB
• 参考文献：Aguilera PA, Fernández A, Reche F, Rumí R (2010) Hybrid Bayesian network classifiers: application to species distribution models. Environ Model Softw 25:1630–1639CrossRef
  Alcalá-Fdez J, Fernandez A, Luengo J, Derrac J, García S, Sánchez L, Herrera F (2011) Keel data-mining software tool: data set repository, integration of algorithms and experimental analysis framework. J Mult Valued Logic Soft Comput 17:255–287
  Bache K, Lichman M (2013) UCI machine learning repository. http://​archive.​ics.​uci.​edu/​ml
  Bernardo JM, Smith AF (2009) Bayesian theory, vol 405. Wiley, New York
  Clemen R, Winkler R (1999) Combining probability distributions from experts in risk analysis. Risk Anal 19(2):187–203
  Fernández A, Gámez JA, Rumí R, Salmerón A (2014) Data clustering using hidden variables in hybrid Bayesian networks. Prog Artif Intell 2:141–152CrossRef
  Fernández A, Nielsen JD, Salmerón A (2010) Learning Bayesian networks for regression from incomplete databases. Int J Uncertain Fuzziness Knowl Based Syst 18:69–86MathSciNet CrossRef
  Fernández A, Pérez-Bernabé I, Rumí R, Salmerón A (2013) Incorporating prior knowledge when learning mixtures of truncated basis functions from data. In: Jaeger M, Nielsen TD, Viappiani P (eds) Proceedings of the 12th Scandinavian AI conference (SCAI’2013) pp 95–104
  Fernández A, Pérez-Bernabé I, Salmerón A (2013) On using the PC algorithm for learning continuous Bayesian networks: an Experimental Analysis. In: Proceedings of the 15th conference of the Spanish Association for Artificial Intelligence (CAEPIA’2013). Lecture Notes in Computer Science, vol 8109. Springer, Berlin, pp 342–351
  Fernández A, Rumí R, del Sagrado J, Salmerón A (2014) Supervised classification using hybrid probabilistic decision graphs. In: Proceedings of the 7th European workshop on probabilistic graphical models (PGM’2014). Lecture Notes in Artificial Intelligence, vol 8754. Springer, Berlin, pp 206–221
  Flores J, Gámez JA, Martínez AM, Salmerón A (2011) Mixtures of truncated exponentials in supervised classification: case study for the naive Bayes and averaged one-dependence estimators. In: Ventura S, Abraham A, Cios KJ, Romero C, Marcelloni F, Benítez JM, Gibaja EL (eds) Proceedings of the 11th international conference on intelligent systems design and applications (ISDA’2011), pp 593–598
  Heckerman D (1997) Bayesian networks for data mining. Data Min Knowl Discov 1:79–119CrossRef
  Kanamori T, Takenouchi T (2013) Improving Logitboost with prior knowledge. Inf Fusion 14:208–219CrossRef
  Langseth H, Nielsen T, Pérez-Bernabé I, Salmerón A (2014) Learning mixtures of truncated basis functions from data. Int J Approx Reason 55:940–956MathSciNet CrossRef MATH
  Langseth H, Nielsen T, Rumí R, Salmerón A (2012) Mixtures of truncated basis functions. Int J Approx Reason 53:212–227MathSciNet CrossRef MATH
  Langseth H, Nielsen T, Salmerón A (2012) Learning mixtures of truncated basis functions from data. In: Cano A, Gómez-Olmedo M, Nielsen TD (eds) Proceedings of the 6th European workshop on probabilistic graphical models (PGM’2012), pp 163–170
  Lauritzen S (1992) Propagation of probabilities, means and variances in mixed graphical association models. J Am Stat Assoc 87:1098–1108MathSciNet CrossRef MATH
  López-Cruz PL, Bielza C, Larrañaga P (2012) Learning mixtures of polynomials from data using B-spline interpolation. In: Cano A, Gómez-Olmedo M, Nielsen TD (eds) Proceedings of the 6th European workshop on probabilistic graphical models (PGM’12), pp 211–218
  López-Cruz PL, Bielza C, Larrañaga P (2014) Learning mixtures of polynomials of multidimensional probability densities from data using B-spline interpolation. Int J Approx Reason 55:989–1010MathSciNet CrossRef MATH
  Luengo JC, Rumí R (2015) Naive Bayes classifier with mixtures of polynomials. In: De Marsico M, Figueiredo M, Fred A (eds) Proceedings of the 4th international conference on pattern recognition applications and methods (ICPRAM’2015), vol 1, pp 14–24
  Moral S, Rumí R, Salmerón A (2001) Mixtures of truncated exponentials in hybrid Bayesian networks. In: Proceedings of the 6th European conference on symbolic and quantitative approaches to reasoning with uncertainty (ECSQARU’2001). Lecture Notes in Artificial Intelligence, vol 2143, pp 135–143
  Moral S, Rumí R, Salmerón A (2003) Approximating conditional MTE distributions by means of mixed trees. In: Proceedings of the 7th European conference on symbolic and quantitative approaches to reasoning with uncertainty (ECSQARU’2003). Lecture Notes in Artificial Intelligence, vol 2711, pp 173–183
  Morales M, Rodríguez C, Salmerón A (2007) Selective naive Bayes for regression using mixtures of truncated exponentials. Int J Uncertain Fuzziness Knowl Based Syst 15:697–716CrossRef MATH
  Pearl J (1988) Probabilistic reasoning in intelligent systems. Morgan-Kaufmann, San MateoMATH
  R Development Core Team (2011) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. http://​www.​R-project.​org/​ . ISBN 3-900051-07-0
  Rumí R, Salmerón A, Moral S (2006) Estimating mixtures of truncated exponentials in hybrid Bayesian networks. Test 15:397–421MathSciNet CrossRef MATH
  Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464MathSciNet CrossRef MATH
  Shenoy P, Shafer G (1990) Axioms for probability and belief function propagation. In: Shachter R, Levitt T, Lemmer J, Kanal L (eds) Uncertainty in artificial intelligence 4. North Holland, Amsterdam, pp 169–198
  Shenoy P, West J (2011) Inference in hybrid Bayesian networks using mixtures of polynomials. Int J Approx Reason 52:641–657MathSciNet CrossRef MATH
  Wong T (2009) Alternative prior assumptions for improving the performance of naïve Bayesian classifiers. Data Min Knowl Discov 18:183–213MathSciNet CrossRef
  Zhang N, Poole D (1996) Exploiting causal independence in Bayesian network inference. J Artif Intell Res 5:301–328MathSciNet MATH
  
• 作者单位：Inmaculada Pérez-Bernabé (1)
  Antonio Fernández (1)
  Rafael Rumí (1)
  Antonio Salmerón (1)
  
  1. Department of Mathematics, University of Almería, 04120, Almería, Spain
  
• 刊物类别：Computer Science
• 刊物主题：Data Mining and Knowledge Discovery
  Computing Methodologies
  Artificial Intelligence and Robotics
  Statistics
  Statistics for Engineering, Physics, Computer Science, Chemistry and Geosciences
  Information Storage and Retrieval
  
• 出版者：Springer Netherlands
• ISSN：1573-756X

文摘

Mixtures of truncated basis functions have been recently proposed as a generalisation of mixtures of truncated exponentials and mixtures of polynomials for modelling univariate and conditional distributions in hybrid Bayesian networks. In this paper we analyse the problem of learning the parameters of marginal and conditional MoTBF densities when both prior knowledge and data are available. Incorporating prior knowledge provide a valuable tool for obtaining useful models, especially in domains of applications where data are costly or scarce, and prior knowledge is available from practitioners. We explore scenarios where the prior knowledge can be expressed as an MoTBF density that is afterwards combined with another MoTBF density estimated from the available data. The resulting model remains within the MoTBF class which is a convenient property from the point of view of inference in hybrid Bayesian networks. The performance of the proposed method is tested in a series of experiments carried out over synthetic and real data.