Abstract
Suppose that we rank-order the conditional probabilities for a group of subjects that are provided from a Bayesian network (BN) model of binary variables. The conditional probability is the probability that a subject has a certain attribute given an outcome of some other variables and the classification is based on the rank-order. Under the condition that the class sizes are equal across the class levels and that all the variables in the model are positively associated with each other, we compared the classification results between models of binary variables which share the same model structure. In the comparison, we used a BN model, called a similar BN model, which was constructed under some rule based on a set of BN models satisfying certain conditions. Simulation results indicate that the agreement level of the classification between a set of BN models and their corresponding similar BN model is considerably high with the exact agreement for about half of the subjects or more and the agreement up to one-class-level difference for about 90% or more.
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References
ALBATINEH, A.N., NIEWIADOMSKA-BUGAJ, M., and MIHALKO, D. (2006), “On Similarity Indices and Correction for Chance Agreement,” Journal of Classification, 23, 301–313.
ANDERSEN, S.K., JENSEN, F.V., OLESEN, K.G., and JENSEN, F. (1989), HUGIN: A Shell for Building Bayesian Belief Universes for Expert Systems [computer program], Aalborg, Denmark: HUGIN Expert Ltd.
BRUSCO, M.J., and STEINLEY, D. (2008), “A Binary Integer Program to Maximize the Agreement Between Partitions,” Journal of Classification, 25, 185–193.
COHEN, J. (1960), “A Coefficient of Agreement for Nominal Scales,” Educational and Psychological Measurement, 20, 37–46.
De FINETTI, B. (1972), Probability, Induction, and Statistics, New York: Wiley.
DEMPSTER, A.P., LAIRD, N.M., and RUBIN, D.B.(1977), “Maximum Likelihood from Incomplete Data Via the EM Algorithm (With Discussion),” Journal of the Royal Sta-tistical Society B, 39, 1–38.
ERGO [computer program] (1991), Baltimore MD: Noetic Systems Inc.
FLEISS, J.L. (1981), Statistical Methods for Rates and Proportions (2nd ed.), New York: Wiley.
HOLLAND, P.W., and ROSENBAUM, P.R. (1986), “Conditional Association and Unidimensionality in Monotone Latent Variable Models,” The Annals of Statistics,14(4), 1523-1543.
JENSEN, F.V.(1996), An Introduction to Bayesian Networks, New York: Springer-Verlag
JUNKER, B.W., and ELLIS, J.L. (1997) “A Characterization of Monotone Unidimensional Latent Variable Models,” The Annals of Statistics, 25(3), 1327–1343.
KIM, S.H. (2002), “Calibrated Initials for an EM Applied to Recursive Models of Categorical Variables,” Computational Statistics and Data Analysis, 40(1), 97–110.
KIM, S.H. (2005), “Stochastic Ordering and Robustness in Classification from a Bayesian Network,” Decision Support Systems, 39, 253–266.
LAURITZEN, S.L., and SPIEGELHALTER, D.J. (1988), “Local Computations with Probabilities on Graphical Structures and Their Application to Expert Systems,” Journal of the Royal Statistical Society B, 50(2), 157–224 .
MESSATFA, H. (1992), “An Algorithm to Maximize the Agreement Between Partitions,” Journal of Classification, 9, 5–15.
MSBNx [computer program] (2001), http://research.microsoft.com/en-us/um/redmond/groups/adapt/msbnx/.
MISLEVY, R.J.(1994), “Evidence and Inference in Educational Assessment,” Psychometrika, 59(4), 439–483.
PEARL, J. (1988), Probabilistic Reasoning In Intelligent Systems: Networks of Plausible Inference, San Mateo CA: Margan Kaufmann.
PIRES, A.M., and BRANCO, J.A. (1997), “Comparison of Multinomial ClassificationRules,” Journal of Classification, 14, 137–145.
SPITZER, R.L., COHEN, J., FLEISS, J.L., and ENDICOTT, J. (1967), “Quantification of Agreement in Psychiatric Diagnosis,” Archives of General Psychiatry, 17, 83–87.
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The authors are grateful to the editor and the three referees for their careful reading of the paper and for their insightful comments and suggestions on it. Our special thanks go to a referee whose suggestion led us to derive the two theorems in Section 3. This work was supported by a grant from Korea Research Foundation Grant (KRF-2010-0023739).
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Kim, SH., Noh, G. Model Similarity and Rank-Order Based Classification of Bayesian Networks. J Classif 30, 428–452 (2013). https://doi.org/10.1007/s00357-013-9140-9
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DOI: https://doi.org/10.1007/s00357-013-9140-9