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On the Relationship Between Dependence Tree Classification Error and Bayes Error Rate
October 2007 (vol. 29 no. 10)
pp. 1866-1868
ASCII Text
x 
 
Kiran S. Balagani, Vir V. Phoha, "On the Relationship Between Dependence Tree Classification Error and Bayes Error Rate," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 10, pp. 1866-1868, October, 2007.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2007.1184,
author = {Kiran S. Balagani and Vir V. Phoha},
title = {On the Relationship Between Dependence Tree Classification Error and Bayes Error Rate},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {29},
number = {10},
issn = {0162-8828},
year = {2007},
pages = {1866-1868},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2007.1184},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - On the Relationship Between Dependence Tree Classification Error and Bayes Error Rate
IS - 10
SN - 0162-8828
SP1866
EP1868
EPD - 1866-1868
A1 - Kiran S. Balagani,
A1 - Vir V. Phoha,
PY - 2007
KW - bayes error rate
KW - entropy
KW - mutual information
KW - classification
KW - dependence tree approximation
VL - 29
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
Wong and Poon [1] showed that Chow and Liu’s tree dependence approximation can be derived by minimizing an upper bound of the Bayes error rate. Wong and Poon’s result was obtained by expanding the conditional entropy H(w|X). We derive the correct expansion of H(w|X) and present its implication.

[1] S.K.M. Wong and F.C.S. Poon, “Comments on Approximating Discrete Probability Distributions with Dependence Trees,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 3, pp. 333-335, Mar. 1989.
[2] C.K. Chow and C.N. Liu, “Approximating Discrete Probability Distributions with Dependence Trees,” IEEE Trans. Information Theory, vol. 14, pp.462-467, May 1968.
[3] J.B. KruskalJr., “On the Shortest Spanning Subtree of a Graph and the Travelling Saleman Problem,” Proc. Conf. Am. Math. Soc., vol. 7, pp. 48-50, 1956.
[4] M.E. Hellman and J. Raviv, “Probability of Error, Equivocation, and the Chernoff Bound,” IEEE Trans. Information Theory, vol. 16, pp. 368-372, May 1970.
[5] T.M. Cover and J.A. Thomas, Elements of Information Theory. Wiley Interscience, 1991.
[6] H. Avi-ltzhak and T. Diep, “Arbitrarily Tight Upper and Lower Bounds on the Bayesian Probability of Error,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 1, pp. 89-91, Jan. 1996.

Index Terms:
bayes error rate, entropy, mutual information, classification, dependence tree approximation
Citation:
Kiran S. Balagani, Vir V. Phoha, "On the Relationship Between Dependence Tree Classification Error and Bayes Error Rate," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 10, pp. 1866-1868, June 2007, doi:10.1109/TPAMI.2007.1184
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