Abstract
Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with state-of-the-art classifiers such as C4.5. This fact raises the question of whether a classifier with less restrictive assumptions can perform even better. In this paper we evaluate approaches for inducing classifiers from data, based on the theory of learning Bayesian networks. These networks are factored representations of probability distributions that generalize the naive Bayesian classifier and explicitly represent statements about independence. Among these approaches we single out a method we call Tree Augmented Naive Bayes (TAN), which outperforms naive Bayes, yet at the same time maintains the computational simplicity (no search involved) and robustness that characterize naive Bayes. We experimentally tested these approaches, using problems from the University of California at Irvine repository, and compared them to C4.5, naive Bayes, and wrapper methods for feature selection.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Binder, J., D. Koller, S. Russell, & K. Kanazawa (1997). Adaptive probabilistic networks with hidden variables. Machine Learning, this issue.
Bouckaert, R. R. (1994). Properties of Bayesian network learning algorithms. In R. López de Mantarás & D. Poole (Eds.), Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (pp. 102–109). San Francisco, CA: Morgan Kaufmann.
Buntine, W. (1991). Theory refinement on Bayesian networks. In B. D. D' Ambrosio, P. Smets, & P. P. Bonissone (Eds.), Proceedings of the Seventh Annual Conference on Uncertainty Artificial Intelligence (pp. 52–60). San Francisco, CA: Morgan Kaufmann.
Buntine, W. (1996). A guide to the literature on learning probabilistic networks from data. IEEE Trans. on Knowledge and Data Engineering, 8, 195–210.
Cestnik, B. (1990). Estimating probabilities: a crucial task in machine learning. In L. C. Aiello (Ed.), Proceedings of the 9th European Conference on Artificial Intelligence (pp. 147–149). London: Pitman.
Chickering, D.M. (1995). Learning Bayesian networks is NP-complete. In D. Fisher & A. Lenz, Learning from Data. Springer-Verlag.
Chickering, D. M. & D. Heckerman (1996). Efficient approximations for the marginal likelihood of incomplete data given a Bayesian network. In E. Horvits & F. Jensen (Eds.), Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (pp. 158–168). San Francisco, CA: Morgan Kaufmann.
Chow, C. K. & C. N. Liu (1968). Approximating discrete probability distributions with dependence trees. IEEE Trans. on Info. Theory, 14, 462–467.
Cooper, G. F. & E. Herskovits (1992). A Bayesian method for the induction of probabilistic networks from data. Machine Learning, 9, 309–347.
Cormen, T. H., C. E. Leiserson, & R. L. Rivest (1990). Introduction to Algorithms. Cambridge, MA: MIT Press.
Cover, T. M. & J. A. Thomas (1991). Elements of Information Theory. New York: John Wiley & Sons.
Dawid, A. P. (1976). Properties of diagnostic data distributions. Biometrics, 32, 647–658.
DeGroot, M. H. (1970). Optimal Statistical Decisions. New York: McGraw-Hill.
Domingos, P. & M. Pazzani (1996). Beyond independence: Conditions for the optimality of the simple Bayesian classifier. In L. Saitta (Ed.), Proceedings of the Thirteenth International Conference on Machine Learning (pp. 105–112). San Francisco, CA: Morgan Kaufmann.
Dougherty, J., R. Kohavi, & M. Sahami (1995). Supervised and unsupervised discretization of continuous features. In A. Prieditis & S. Russell (Eds.), Proceedings of the Twelfth International Conference on Machine Learning (pp. 194–202). San Francisco, CA: Morgan Kaufmann.
Duda, R. O. & P. E. Hart (1973). Pattern Classification and Scene Analysis. New York: John Wiley & Sons.
Ezawa, K. J. & T. Schuermann (1995). Fraud/uncollectable debt detection using a Bayesian network based learning system: A rare binary outcome with mixed data structures. In P. Besnard & S. Hanks (Eds.), Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (pp. 157–166). San Francisco, CA: Morgan Kaufmann.
Fayyad, U. M. & K. B. Irani (1993). Multi-interval discretization of continuous-valued attributes for classification learning. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence (pp. 1022–1027). San Francisco, CA: Morgan Kaufmann.
Friedman, J. (1997a). On bias, variance, 0/1-loss, and the curse-of-dimensionality. Data Mining and Knowledge Discovery, 1, 55–77.
Friedman, N. (1997b). Learning belief networks in the presence of missing values and hidden variables. In D. Fisher (Ed.), Proceedings of the Fourteenth International Conference on Machine Learning (pp. 125–133). San Francisco, CA: Morgan Kaufmann.
Friedman, N. & M. Goldszmidt (1996a). Building classifiers using Bayesian networks. In Proceedings of the National Conference on Artificial Intelligence (pp. 1277–1284). Menlo Park, CA: AAAI Press.
Friedman, N. & M. Goldszmidt (1996b). Discretization of continuous attributes while learning Bayesian networks. In L. Saitta (Ed.), Proceedings of the Thirteenth International Conference on Machine Learning (pp. 157–165). San Francisco, CA: Morgan Kaufmann.
Friedman, N. & M. Goldszmidt (1996c). Learning Bayesian networks with local structure. In E. Horvits & F. Jensen (Eds.), Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (pp. 252–262). San Francisco, CA: Morgan Kaufmann.
Geiger, D. (1992). An entropy-based learning algorithm of Bayesian conditional trees. In D. Dubois, M. P. Wellman, B. D. D' Ambrosio, & P. Smets (Eds.), Proceedings of the Eighth Annual Conference on Uncertainty Artificial Intelligence (pp. 92–97). San Francisco, CA: Morgan Kaufmann.
Geiger, D. & D. Heckerman (1996). Knowledge representation and inference in similarity networks and Bayesian multinets. Artificial Intelligence, 82, 45–74.
Geiger, D., D. Heckerman, & C. Meek (1996). Asymptotic model selection for directed graphs with hidden variables. In E. Horvits & F. Jensen (Eds.), Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (pp. 283–290). San Francisco, CA: Morgan Kaufmann.
Heckerman, D. (1991). Probabilistic Similarity Networks. Cambridge, MA: MIT Press.
Heckerman, D. (1995). A tutorial on learning Bayesian networks. Technical Report MSR-TR–95–06, Microsoft Research.
Heckerman, D. & D. Geiger (1995). Learning Bayesian networks: a unification for discrete and Gaussian domains. In P. Besnard & S. Hanks (Eds.), Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (pp. 274–284). San Francisco, CA: Morgan Kaufmann.
Heckerman, D., D. Geiger, & D. M. Chickering (1995). Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning, 20, 197–243.
John, G. & R. Kohavi (1997). Wrappers for feature subset selection. Artificial Intelligence. Accepted for publication. A preliminary version appears in Proceedings of the Eleventh International Conference on Machine Learning, 1994, pp. 121–129, under the title “Irrelevant features and the subset selection problem”.
John, G. H. & P. Langley (1995). Estimating continuous distributions in Bayesian classifiers. In P. Besnard & S. Hanks (Eds.), Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (pp. 338–345). San Francisco, CA: Morgan Kaufmann.
Kohavi, R. (1995). A study of cross-validation and bootstrap for accuracy estimation and model selection. In Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (pp. 1137–1143). San Francisco, CA: Morgan Kaufmann.
Kohavi, R., G. John, R. Long, D. Manley, & K. Pfleger (1994). MLC++: A machine learning library in C++. In Proc. Sixth International Conference on Tools with Artificial Intelligence (pp. 740–743). IEEE Computer Society Press.
Kononenko, I. (1991). Semi-naive Bayesian classifier. In Y. Kodratoff (Ed.), Proc. Sixth European Working Session on Learning (pp. 206–219). Berlin: Springer-Verlag.
Kullback, S. & R. A. Leibler (1951). On information and sufficiency. Annals of Mathematical Statistics, 22, 76–86.
Lam, W. & F. Bacchus (1994). Learning Bayesian belief networks. An approach based on the MDL principle. Computational Intelligence, 10, 269–293.
Langley, P., W. Iba, & K. Thompson (1992). An analysis of Bayesian classifiers. In Proceedings, Tenth National Conference on Artificial Intelligence (pp. 223–228). Menlo Park, CA: AAAI Press.
Langley, P. & S. Sage (1994). Induction of selective Bayesian classifiers. In R. López de Mantarás & D. Poole (Eds.), Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (pp. 399–406). San Francisco, CA: Morgan Kaufmann.
Lauritzen, S. L. (1995). The EM algorithm for graphical association models with missing data. Computational Statistics and Data Analysis, 19, 191–201.
Lewis, P. M. (1959). Approximating probability distributions to reduce storage requirements. Information and Control, 2, 214–225.
Murphy, P. M. & D. W. Aha (1995). UCI repository of machine learning databases. http://www.ics.uci. edu/~mlearn/MLRepository.html.
Pazzani, M. J. (1995). Searching for dependencies in Bayesian classifiers. In D. Fisher & H. Lenz (Eds.), Proceedings of the fifth International Workshop on Artificial Intelligence and Statistics, Ft. Lauderdale, FL.
Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. San Francisco, CA: Morgan Kaufmann.
Quinlan, J. R. (1993). C4.5: Programs for Machine Learning. San Francisco, CA: Morgan Kaufmann.
Ripley, B. D. (1996). Pattern recognition and neural networks. Cambridge: Cambridge University Press.
Rissanen, J. (1978). Modeling by shortest data description. Automatica, 14, 465–471.
Rubin, D. R. (1976). Inference and missing data. Biometrica, 63, 581–592.
Singh, M. & G.M. Provan (1995). A comparison of induction algorithms for selective and non-selective Bayesian classifiers. In A. Prieditis & S. Russell (Eds.), Proceedings of the Twelfth International Conference on Machine Learning (pp. 497–505). San Francisco, CA: Morgan Kaufmann.
Singh, M. & G. M. Provan (1996). Efficient learning of selective Bayesian network classifiers. In L. Saitta (Ed.), Proceedings of the Thirteenth International Conference on Machine Learning (pp. 453–461). San Francisco, CA: Morgan Kaufmann.
Spiegelhalter, D. J., A. P. Dawid, S. L. Lauritzen, & R. G. Cowell (1993). Bayesian analysis in expert systems. Statistical Science, 8, 219–283.
Suzuki, J. (1993). A construction of Bayesian networks from databases based on an MDL scheme. In D. Heckerman & A. Mamdani (Eds.), Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (pp. 266–273). San Francisco, CA: Morgan Kaufmann.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Friedman, N., Geiger, D. & Goldszmidt, M. Bayesian Network Classifiers. Machine Learning 29, 131–163 (1997). https://doi.org/10.1023/A:1007465528199
Issue Date:
DOI: https://doi.org/10.1023/A:1007465528199