Abstract
Naive Bayes is a relatively simple classification method to, e.g., rate TV programs as interesting or uninteresting to a user. In case the training set consists of instances, chosen randomly from the instance space, the posterior probability estimates are random variables. Their statistical properties can be used to calculate confidence intervals around them, enabling more refined classification strategies than the usual argmax-operator. This may alleviate the cold-start problem and provide additional feedback to the user.
In this paper, we give an explicit expression to estimate the variances of the posterior probability estimates from the training data and investigate the strategy that refrains from classification in case the confidence interval around the largest posterior probability overlaps with any of the other intervals.
We show that the classification error rate can be significantly reduced at the cost of a lower coverage, i.e., the fraction of classifiable instances, in a TV-program recommender.
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
Berikov, V.B.: An approach to the evaluation of the performance of a discrete classifier. Pattern Recognition Letters 23(1-3), 227–233 (2002)
Cestnik, B.: Estimating probabilities: a crucial task in machine learning. In: Proceedings of the European Conference on Artificial Intelligence (ECAI 1990), Stockholm, Norway, pp. 147–149, August 6–10 (1990)
Domingos, P., Pazzani, M.: On the optimality of the simple Bayesian classifier under zero-one loss. Machine Learning 29(2-3), 103–130 (1997)
Elkan, C.: The foundations of cost-sensitive learning. In: Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI 2001), Seattle, Washington, pp. 973–978, August 4–10 (2001)
Gärtner, T., Wu, S., Flach, P.A.: Data mining on the Sisyphus dataset: evaluation and integration of results. In: Giraud-Carrier, C., Lavrac, N., Moyle, S. (eds.) Integrating Aspects of Data Mining, Decision Support and Meta-Learning, pp. 69–80 (2001)
Hand, D.J., Yu, K.: Idiot’s Bayes – not so stupid after all? International Statistical Review 69(3), 385–398 (2001)
Kononenko, I.: Semi-naive Bayesian classifier. In: Kodratoff, Y. (ed.) EWSL 1991. LNCS, vol. 482, pp. 206–219. Springer, Heidelberg (1991)
Kononenko, I.: Machine learning for medical diagnosis: history, state of the art and perspective. Artificial Intelligence in Medicine 23(1), 89–109 (2001)
Kukar, M.: Making reliable diagnoses with machine learning: a case study. In: Quaglini, S., Barahona, P., Andreassen, S. (eds.) AIME 2001. LNCS (LNAI), vol. 2101, pp. 88–98. Springer, Heidelberg (2001)
Mitchell, T.M.: Machine Learning. McGraw-Hill, New York (1997)
Ramoni, M., Sebastiani, P.: Robust Bayes classifiers. Artificial Intelligence 125, 209–226 (2001)
Zaffalon, M.: The naive credal classifier. Journal of Statistical Planning and Inference 105(1), 5–21 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pronk, V., Gutta, S.V.R., Verhaegh, W.F.J. (2005). Incorporating Confidence in a Naive Bayesian Classifier. In: Ardissono, L., Brna, P., Mitrovic, A. (eds) User Modeling 2005. UM 2005. Lecture Notes in Computer Science(), vol 3538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527886_41
Download citation
DOI: https://doi.org/10.1007/11527886_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27885-6
Online ISBN: 978-3-540-31878-1
eBook Packages: Computer ScienceComputer Science (R0)