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A conditional independence algorithm for learning undirected graphical models. (English) Zbl 1186.68356
Summary: When it comes to learning graphical models from data, approaches based on conditional independence tests are among the most popular methods. Since Bayesian networks dominate research in this field, these methods usually refer to directed graphs, and thus have to determine not only the set of edges, but also their direction. At least for a certain kind of possibilistic graphical models, however, undirected graphs are a much more natural basis. Hence, in this area, algorithms for learning undirected graphs are desirable, especially, since first learning a directed graph and then transforming it into an undirected one wastes resources and computation time. In this paper, I present a general algorithm for learning undirected graphical models, which is strongly inspired by the well-known Cheng-Bell-Liu algorithm for learning Bayesian networks from data. Its main advantage is that it needs fewer conditional independence tests, while it achieves results of comparable quality.
MSC:
68T05Learning and adaptive systems
68R10Graph theory in connection with computer science (including graph drawing)
68W05Nonnumerical algorithms
References:
[1]Agosta, J. M.: Intel technol. J., Intel technol. J. 8, No. 4, 361-372 (2004)
[2]Borgelt, C.; Kruse, R.: Evaluation measures for learning probabilistic and possibilistic networks, , 1034-1038 (1997)
[3]Borgelt, C.; Kruse, R.: Efficient maximum projection of database-induced multivariate possibility distributions, (1998)
[4]Borgelt, C.; Kruse, R.: Graphical models — methods for data analysis and mining, (2002) · Zbl 1017.62002
[5]Castillo, G.: Adaptive learning algorithms for Bayesian network classifiers, AI commun. 21, No. 1, 87-88 (2008)
[6]Charitos, T.; Van Der Gaag, L. C.; Visscher, S.; Schurink, K. A. M.; Lucas, P. J. F.: A dynamic Bayesian network for diagnosing ventilator-associated pneumonia in ICU patients, Expert systems appl. 36, No. 2.1, 1249-1258 (2007)
[7]Chickering, D. M.: Optimal structure identification with greedy search, J. Mach learn. Res. 3, 507-554 (2002) · Zbl 1084.68519 · doi:10.1162/153244303321897717
[8]Cho, S. -J.; Kim, J. H.: Bayesian network modeling of strokes and their relationship for on-line handwriting recognition, Pattern recogn. 37, No. 2, 253-264 (2003) · Zbl 1059.68103 · doi:10.1016/j.patcog.2003.01.001
[9]Cooper, G. F.; Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data, Mach learn. 9, 309-347 (1992) · Zbl 0766.68109
[10]Cheng, J.; Bell, D. A.; Liu, W.: Learning belief networks from data: an information theory based approach, , 325-331 (1997)
[11]Cheng, J.; Greiner, R.; Kelly, J.; Bell, D. A.; Liu, W.: Learning Bayesian networks from data: an information theory based approach, Artificial intelligence 137, No. 1 – 2, 43-90 (2002) · Zbl 0995.68114 · doi:10.1016/S0004-3702(02)00191-1
[12]Buntine, W.: Operations for learning with graphical models, J. artificial intelligence res. 2, 159-225 (1994)
[13]De Campos, L. M.; Huete, J. F.; Moral, S.: Independence in uncertainty theories and its application to learning belief networks, DRUMS handbook on abduction and learning, 391-434 (2000) · Zbl 0970.68133
[14]Castillo, E.; Gutierrez, J. M.; Hadi, A. S.: Expert systems and probabilistic network models, (1997)
[15]Chow, C. K.; Liu, C. N.: Approximating discrete probability distributions with dependence trees, IEEE trans. Inform. theory 14, No. 3, 462-467 (1968) · Zbl 0165.22305 · doi:10.1109/TIT.1968.1054142
[16]Frankel, J.; Webster, M.; King, S.: Articulatory feature recognition using dynamic Bayesian networks, Comput. speech and lang. 21, No. 4, 620-640 (2007)
[17]Gamez, J. A.; Moral, S.; Salmeron, A.: Advances in Bayesian networks, (2004)
[18]J. Gebhardt, Learning from data: Possibilistic graphical models, Habilitation Thesis, University of Braunschweig, Germany, 1997
[19], , 46 (2004)
[20]Heckerman, D.; Geiger, D.; Chickering, D. M.: Learning Bayesian networks: the combination of knowledge and statistical data, Mach learn. 20, 197-243 (1995) · Zbl 0831.68096
[21]Jensen, F. V.: Bayesian networks and decision graphs, (2001)
[22], Learning in graphical models (1998)
[23]Khanafar, R. M.; Solana, B.; Triola, J.; Barco, R.; Moltsen, L.; Altman, Z.; Lazaro, P.: Automated diagnosis for UMTS networks using a Bayesian network approach, IEEE trans. Veh. technol. 57, No. 4, 2451-2461 (2008)
[24]Kim, S.; Imoto, S.; Miyano, S.: Dynamic Bayesian network and nonparametric regression for nonlinear modeling of gene networks from time series gene expression data, Biosystems 75, No. 1 – 3, 57-65 (2004)
[25]Lauritzen, S. L.: Graphical models, (1996)
[26]Neapolitan, R. E.: Learning Bayesian networks, (2004)
[27]Niculescu, R. S.; Mitchell, T. M.; Rao, R. B.: Bayesian network learning with parameter constraints, J. Mach learn. Res. 7, 1357-1383 (2006) · Zbl 1222.68275 · doi:http://www.jmlr.org/papers/v7/niculescu06a.html
[28]Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference, (1988)
[29]Pernkopf, F.: Detection of surface defects on raw steel blocks using Bayesian network classifiers, Pattern anal. Appl. 7, No. 3, 333-342 (2004)
[30]Rasmussen, L. K.: Blood group determination of danish jersey cattle in the F-blood group system, Dina res. Rep. 8 (1992)
[31]Robles, V.; Larrañaga, R.; Pena, J.; Menasalvas, E.; Perez, M.; Herves, V.; Wasilewska, A.: Bayesian network multi-classifiers for protein secondary structure identification, Artificial intelligence med. 31, No. 2, 117-136 (2004)
[32]Roos, T.; Wettig, H.; Grünwald, P.; Myllymäki, P.; Tirri, H.: On discriminative Bayesian network classifiers and logistic regression, Mach learn. 65, No. 1, 31-78 (2005)
[33]Schneiderman, H.: Learning a restricted Bayesian network for object recognition, , 639-646 (2004)
[34]Singh, M.; Valtorta, M.: An algorithm for the construction of Bayesian network structures from data, , 259-265 (1993)
[35]Spirtes, P.; Glymour, C.; Scheines, R.: Causation, prediction, and search, Lecture notes in statist. 81 (1993) · Zbl 0806.62001
[36]H. Steck, Constraint-based structural learning in Bayesian networks using finite data sets, PhD thesis, TU München, Germany, 2001
[37]Tsamardinos, I.; Brown, L. E.; Aliferis, C. F.: The MAX – MIN Hill-climbing Bayesian network structure learning algorithm, Mach learn. 65, No. 1, 31-78 (2006)
[38]Whittaker, J.: Graphical models in applied multivariate statistics, (1990)