Abstract
In this work, two novel sequential algorithms for learning Bayesian networks are proposed. The presented sequential search methods are an adaptation of a pair of algorithms proposed to feature subset selection: Sequential Forward Floating Selection and Sequential Backward Floating Selection. As far as we know, these algorithms have never been used for learning Bayesian networks. An empirical comparison among the results of the proposed algorithms and the results of two sequential algorithm (the classical B-algorithm and its extension, the B3 algorithm) is carried out over four databases from literature. The results show promising results for the floating approach to the learning Bayesian network problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. Abramson, J. M. Brown, W. Edwards, A. Murphy, and R. L. Winkler, ‘Hailfinder: A Bayesian system for forecasting severe weather’, International Journal of Forecasting, 12, 57–71, (1996) .
S. Acid, L. M. de Campos, and J. F. Huete, ‘The search of causal orderings: a short cut for learning belief networks’, in Proceedings of the Sixth European Conference on Symbolic and Quantitative Approache to Reasoning with Uncertainty, pp. 228–239, (2001) .
I.A. Beinlinch, H.J. Suermondt, R.M. Chavez, and G.F. Coooper, ‘The ALARM monitoring system: a case study with two probabilistic inference techniques for belief networks’, in Proceedings of the Second European Conference on Artificial Intelligence in Medicine, pp. 247–257, (1989) .
J. Binder, D. Koller, S. Russell, and K. Kanazawa, ‘Adaptive probabilistic networks with hidden variables’, Machine Learning, 29(2–3), 213–244, (1997).
R. Blanco, I. Inza, and P. Larrañaga, ‘Learning Bayesian networks in the space of structures by estimation of distribution algorithms’, International Journal of Intelligent Systems, 18, 205–220, (2003).
C. Borgelt and R. Kruse, ‘An empirical investigation of the K2 metric’, in Proceedings of the Sixth European Conference on Symbolic and Quantitative Approache to Reasoning with Uncertainty, pp. 240–251, (2001).
W. Buntine, ‘Theory refinement in Bayesian networks’, in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence, pp. 52–60, (1991) .
W. Buntine, ‘A guide to the literature on learning probabilistic networks from data’, IEEE Transactions on Knowledge and Data Engineering, 8(2), 195–210, (1996).
E. Castillo, J.M. Gutiérrez, and A.S. Hadi, Expert Systems and Probabilistic Network Models, Springer-Verlag, New York, 1997.
J. Cheng, R. Greiner, J. Kelly, D. Bell, and W. Liu, ‘Learning Bayesian networks from data: an information-theory based approach’, Artificial Intelligence, 137(1–2), 43–90, (2002).
D.M. Chickering, ‘Learning equivalence classes of Bayesian network structures’, Journal of Machine Learning Research, 2, 445–498, (2002) .
D.M. Chickering, D. Geiger, and D. Heckerman, ‘Learning Bayesian networks is NP-hard’, Technical Report MSR-TR-94–17, Microsoft Research, Advanced Technology Division, Microsoft Corporation, Redmond, WA, (1994) .
D.M. Chickering, D. Geiger, and D. Heckerman, ‘Learning Bayesian networks: Search methods and experimental results’, in Preliminary Papers of the Fifth International Workshop on Artificial Intelligence and Statistics, pp. 112–128, (1995) .
G.F. Cooper and E.A. Herskovits, ‘A Bayesian method for the induction of probabilistic networks from data’, Machine Learning, 9, 309–347, (1992) .
C. Cotta and J. Muruzábal, ‘Towards more efficient evolutionary induction of Bayesian networks’, in Parallel Problem Solving From Nature VIII. Lecture Notes in Computer Science 2439, pp. 730–739, (2002) .
R.G. Cowell, ‘Conditions under which conditional independence and scoring methods lead to identical selection of Bayesian network models’, in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, pp. 91–97, (2001) .
A.P. Dawid, ‘Conditional independence in statistical theory’, Journal of the Royal Statistics Society, Series B, 41, 1–31, (1979) .
L.M. de Campos, J.M. Fernández-Luna, J.J. Gámez, and J.M. Puerta, ‘Ant colony optimization for learning Bayesian networks’, International Journal on Artificial Reasoning, 31(3), 109–136, (2002) .
L.M. de Campos and J.F. Huete, ‘A new approach for learning belief networks using independence criteria’, International Journal of Approximate Reasoning, 24(1), 11–37, (2000).
L.M. de Campos and J.M. Puerta, ‘Stochastic local algorithms for learning belief networks: searching in the space of the orderings, symbolic and quantitative approaches to reasoning with uncertainty’, Lecture Notes in Artificial Intelligence 2143, 228–239, (2001).
N. Friedman, M. Goldszmidt, and A. Wyner, ‘On the application of the bootstrap for computing confidence measures on features of induced Bayesian networks’, in Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, (1999) .
N. Friedman and D. Koller, ‘Being Bayesian about network structure: A Bayesian approach to structure discovery in Bayesian networks’, Machine Learning, 50(1–2), 95–125, (2003).
S. Gillispie and M. Perlman, ‘Enumerating Markov equivalence classes of acyclic digraph models’, in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, pp. 171–177, (2001).
J. Habrant, ‘Structure learning of Bayesian networks from databases by genetic algorithms’, in Proceedings of the International Conference on Enterprise Information Systems, (1999) .
D. Heckerman, ‘A tutorial on learning with Bayesian networks’, Technical Report MSR-TR-95–06, Microsoft Advanced Technology Division, Microsoft Corporation, Seattle, Washington, (1995) .
D. Heckerman and D. Geiger, ‘Likelihoods and parameters priors for Bayesian networks’, Technical Report MST-TR-95–54, Microsoft Advanced Technology Division, Microsoft Corporation, Seattle, Washington, (1995) .
D. Heckerman, D. Geiger, and D.M. Chickering, ‘Learning Bayesian networks: The combination of knowledge and statistical data’, Machine Learning, 20, 197–243, (1995) .
E.A. Herskovits and G.F. Cooper, ‘Kutató: An entropy-driven system for construction of probabilistic expert systems from database’, in Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence, pp. 54–62, (1990).
A.L. Jensen and F.V. Jensen, ‘MIDAS — An influence diagram for management of mildew in winther wheat’, in Proceedings of the Twelfeth Conference on Uncertainty in Artificial Intelligence, pp. 349–356, San Francisco, (1996) . Morgan Kaufmann.
F.V. Jensen, Bayesian Networks and Decision Graphs, Springer Verlag, 2001.
J. Kittler, ‘Feature set search algorithms’, in Pattern Recognition and Signal Processing, ed., C.H. Chen, pp. 41–60. Sithoff and Noordhoff, (1978) .
T. Kočka and R. Castelo, ‘Improved learning of Bayesian networks’, in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, pp. 269–276, (2001).
P. Larrañaga, C.M.H. Kuijpers, R.H. Murga, and Y. Yurramendi, ‘Learning Bayesian network structures by searching for the best ordering with genetic algorithms’, IEEE Transactions on Systems, Man, and Cybernetics — Part A: Systems and Humans, 26(4), 487–493, (1996) .
P. Larrañaga, M. Poza, Y. Yurramendi, R.H. Murga, and C.M.H. Kuijpers, ‘Structure learning of Bayesian networks by genetic algorithms: A performance analysis of control parameters’, IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(9), 912–926, (1996).
H.B. Mann and D.R. Whitney, ‘On a test of whether one of two random variables is stochastically larger than the other’, Annals of Mathematical Statistics, 18, 50–60, (1947) .
J.W. Myers, K.B. Laskey, and T. Levitt, ‘Learning Bayesian networks from incomplete data with stochastic search algorithms’, in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, pp. 476–485, (1999).
J. Pearl, Probabilistic Reasoning in Intelligent Systems, Morgan Kaufmann, 1988.
J.M. Peña, J.A. Lozano, and P. Larrañaga, ‘Unsupervised learning of Bayesian networks via estimation of distribution algorithms’, in Proceedings of the First European Workshop on Probabilistics Graphical Models, pp. 144–151, (2002) .
P. Pudil, J. Novovicova, and J. Kittler, ‘Floating search methods in feature selection’, Pattern Recognition Letters, 15(1), 1119–1125, (1994).
R.W. Robinson, ‘Counting unlabelled acyclic digraphs’, in Lecture Notes in Mathematics: Combinatorial Mathematics V, pp. 28–43. Springer-Verlag, (1977) .
G. Schwarz, ‘Estimating the dimension of a model’, Annals of Statistics, 7(2), 461–464, (1978) .
C.E. Shannon, ‘A mathematical theory of communication’, The Bell System Technical Journal, 27, 379–423, (1948) .
P. Spirtes, C. Glymour, and R. Scheines, Causation, Prediction, and Search, Lecture Notes in Statistics 81, Springer-Verlag, 1993.
S.D. Stearns, ‘On selecting features for pattern classifiers’, in Third International Conference on Pattern Recognition, pp. 71–75, (1976).
H. Steck, ‘On the use of skeletons when learning in Bayesian networks’, in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, pp. 558–565, (2000).
J. Tian, ‘A branch and bound algorithm for MDL learning Bayesian networks’, in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, pp. 580–588, (2000).
G. Wahba, ‘Comments on ’monotone regression splines in action’ , Statistical Science, 3, 456–458, (1988) .
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Blanco, R., Inza, I., Larrañaga, P. (2004). Learning Bayesian Networks by Floating Search Methods. In: Gámez, J.A., Moral, S., Salmerón, A. (eds) Advances in Bayesian Networks. Studies in Fuzziness and Soft Computing, vol 146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39879-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-39879-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05885-1
Online ISBN: 978-3-540-39879-0
eBook Packages: Springer Book Archive