Abstract
The marginal likelihood of the data computed using Bayesian score metrics is at the core of score+search methods when learning Bayesian networks from data. However, common formulations of those Bayesian score metrics depend of free parameters which are hard to asses. Recent theoretical and experimental works have also shown as the commonly employed BDeu score metric is strongly biased by the particular assignments of its free parameter known as the equivalent sample size and, also, as an optimal selection of this parameter depends of the underlying distribution. This sensibility causes that wrong choices of this parameter lead to inferred models which do not properly represent the distribution generating the data even with large sample sizes. To overcome this issue we introduce here an approach which tries to marginalize this free parameter with a simple averaging method. As experimentally shown, this approach robustly performs as well as an optimum selection of this parameter while it prevents from the choice of wrong settings for this widely applied Bayesian score metric.
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References
Abellán, J., Moral, S.: A new score for independence based on the imprecise dirichlet model. In: International Symposium on Imprecise Probabilities and their Applications, pp. 1–10 (2005)
Buntine, W.: Theory refinement on Bayesian networks. In: Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence, San Francisco, CA, USA, pp. 52–60 (1991)
Cooper, G., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 309–347 (1992)
Heckerman, D., Geiger, D., Chickering, D.: Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning 20(3), 197–243 (1995)
Moral, S.: An empirical comparison of score measures for independence. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2004, pp. 1307–1314 (2004)
Pearl, J.: Probabilistic Reasoning with Intelligent Systems. Morgan-Kaufman, San Francisco (1988)
Scott, J.G., Berger, J.O.: An exploration of aspects of Bayesian multiple testing. Journal of Statistical Planning and Inference 136(7), 2144–2162 (2006)
Silander, T., Kontkanen, P., Myllymaki, P.: On sensitivity of the MAP Bayesian network structure to the equivalent sample size parameter. In: Proceedings of the Twenty-Third Annual Conference on Uncertainty in Artificial Intelligence (UAI 2007), pp. 360–367. AUAI Press, Corvallis (2007)
Steck, H.: Learning the Bayesian network structure: Dirichlet prior vs data. In: McAllester, D.A., Myllymäki, P. (eds.) UAI, pp. 511–518. AUAI Press (2008)
Steck, H., Jaakkola, T.: On the Dirichlet prior and Bayesian regularization. In: Becker, S., Thrun, S., Obermayer, K. (eds.) NIPS, pp. 697–704. MIT Press, Cambridge (2002)
Ueno, M.: Learning networks determined by the ratio of prior and data. In: Grnwald, P., Spirtes, P. (eds.) Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence (UAI 2010). AUAI Press (2010)
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Cano, A., Gómez-Olmedo, M., Masegosa, A.R., Moral, S. (2011). Locally Averaged Bayesian Dirichlet Metrics. In: Liu, W. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2011. Lecture Notes in Computer Science(), vol 6717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22152-1_19
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DOI: https://doi.org/10.1007/978-3-642-22152-1_19
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