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Keywords:
Bayesian networks; Bayesian information criterion; sociology; structural learning
Bayesian networks; Bayesian information criterion; sociology; structural learning
Summary:
One of the most frequently employed criteria for the structural learning of Bayesian networks (BNs) is the Bayesian Information Criterion (BIC). The objective is to identify a model that exhibits an optimal balance between the fit to the training data, as measured by the log-likelihood, and the model's complexity, as quantified by the number of model parameters. A significant challenge associated with this approach pertains to the exponential increase in the number of parameters required for conditional probability tables (CPTs) as the number of parents of each node increases. This phenomenon leads to a substantial growth in the complexity of the CPTs, which serve as the fundamental building blocks of BNs. However, there exist models of CPTs whose number of parameters grows linearly with the number of parents, and they often represent a better fit to data than general CPTs. In this paper, we examine models with CPTs, either in their general form or in the form corresponding to multinomial logistic regression (MLR) or ordinal logistic regression (OLR). We employ data from a sociological study entitled “Dividing Lines in Czech Society” to demonstrate the enhancement through the incorporation of MLR and OLR models as CPTs within the framework of BN structural learning.
References:
[1] Agresti, A.: Categorical Data Analysis. Third edition. John Wiley and Sons, Hoboken, NJ 2013.
[2] Buchtík, M.: Různá vyprávění o jedné společnosti. Friedrich-Ebert-Stiftung and Masarykova demokratická akademie, Praha 2023.
[3] Cussens, J.: Bayesian network learning with cutting planes. In: Proc. 27th Conference on Uncertainty in Artificial Intelligence, (F. Cozman and A. Pfeffer, eds.), AUAI Press, Corvallis 2011, pp. 153-160. DOI
[4] Campos, C. P. de, Scanagatta, M., Corani, G., Zaffalon, M.: Entropy-based pruning for learning Bayesian networks using BIC. Artificial Intelligence 260 (2018), 42-50. DOI
[5] Díez, F. J., Galán, S. F.: An efficient factorization for the noisy MAX. Int. J. Intell. Systems 18 (2003), 165-177. DOI
[6] Epskamp, S., Cramer, A. O. J., Waldorp, L. J., Schmittmann, V. D., Borsboom, D.: Network visualizations of relationships in psychometric data. J. Statist. Software 48 (2012), 4, 1-18. DOI
[7] Fruchterman, T. M. J., Reingold, E. M.: Graph drawing by force-directed placement. Software: Practice Experience 21 (1991), 11, 1129-1164. DOI
[8] Holm, S.: A simple sequentially rejective multiple test procedure. Scand. J. Statist. 6 (1979), 65-70. DOI
[9] Jensen, F. V., Nielsen, T. D.: Bayesian Networks and Decision Graphs. Second edition. Information Science and Statistics, Springer New York, NY 2007. DOI
[10] Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. The MIT Press, 2009.
[11] Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco 1988. Zbl 0746.68089
[12] Rijmen, F.: Bayesian networks with a logistic regression model for the conditional probabilities. Int. J. Approx. Reasoning 48 (2008), 2, 659-666. In memory of Philippe Smets 1938-2005. DOI | Zbl 1184.62039
[13] Schwarz, G.: Estimating the dimension of a model. Ann. Statist. 6 (1978), 2, 461-464. DOI | Zbl 0379.62005
[14] Sharma, C., Liao, Z. A., Cussens, J., Beek, P. van: A score-and-search approach to learning Bayesian networks with noisy-or relations. In: Pro. 10th International Conference on Probabilistic Graphical Models (PGM 2020). Proc. Machine Learning Research 138 (2020), pp. 413-42. DOI
[15] Vomlel, J., Kratochvíl, V., Kratochvíl, F.: Structural learning of mixed noisy-OR Bayesian networks. Int. J. Approx. Reasoning 161 (2023), 108990. DOI
[16] Vomlel, J., Kuběna, A., Šmíd, M., Weinerova, J.: Uncovering relationships using bayesian networks: A case study on conspiracy theories. In: Proc. 12th International Conference on Probabilistic Graphical Models. Proc. Machine Learning Research (J. Kwisthout and S. Renooij, eds.), PMLR 246 (2024), pp. 470-485. DOI
[17] Vomlel, J., Tichavský, P.: Probabilistic inference with noisy-threshold models based on a CP tensor decomposition. Int. J. Approx. Reasoning 55 (2014), 4, 1072-1092. DOI
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