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Comments on Approximating Discrete Probability Distributions with Dependence Trees
March 1989 (vol. 11 no. 3)
pp. 333-335

C.K. Chow and C.N. Liu (1968) introduced the notion of three dependence to approximate a kth-order probability distribution. More recently, A.K.C. Wong and C.C. Wang (1977) proposed a different product approximation. The present authors show that the tree dependence approximation suggested by Chow and Liu can be derived by minimizing an upper bound of the Bayes error rate under certain assumptions. They also show that the method proposed by Wong and Wang does not necessarily lead to fewer misclassifications, because it is a special case of such a minimization procedure.

[1] P. M. Lewis, "Approximating probability distributions to reduce storage requirement,"Inform. and Contr., vol. 2, pp. 214-225, Sept. 1959.
[2] C. K. Chow and C. N. Liu, "Approximating discrete probability distributions with dependence trees,"IEEE Trans. Inform. Theory, vol. IT-14, no. 3. May 1968.
[3] J. B. Kruskal, Jr., "On the shortest spanning subtree of a graph and the traveling salesman problem,"Proc. Amer. Math. Soc., vol. 7, pp. 48-50, 1956.
[4] A. K. C. Wong and C. C. Wang, "Classification of discrete biomedical data with error probability minimax," inProc. SeventthInt. Conf. Cybern. Soc., Washington, DC, Sept. 1977, pp. 19-21.
[5] D. C. C. Wang and A. K. C. Wong, "Classification of discrete data with feature space transformation,"IEEE Trans. Automat. Contr., vol. AC-24, no. 3, pp. 434-437, 1979.
[6] M. E. Hellman, "Probability of error, equivocation, and Chernoff bound,"IEEE Trans. Inform. Theory, vol. 16, pp. 368-372, July 1970.

Index Terms:
pattern recognition; classification; discrete probability distributions; probability distribution; product approximation; tree dependence approximation; Bayes error rate; minimization; approximation theory; Bayes methods; error statistics; minimisation; pattern recognition; probability; trees (mathematics)
Citation:
S.K.M. Wong, F.C.S. Poon, "Comments on Approximating Discrete Probability Distributions with Dependence Trees," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 3, pp. 333-335, March 1989, doi:10.1109/34.21803
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