Abstract
Bayesian decision theory is a fundamental decision-making approach under the probability framework. In an ideal situation when all relevant probabilities were known, Bayesian decision theory makes optimal classification decisions based on the probabilities and costs of misclassifications. In the following, we demonstrate the basic idea of Bayesian decision theory with multiclass classification.
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References
Bishop CM (2006) Pattern recognition and machine learning. Springer, New York, NY
Chickering DM, Heckerman D, Meek C (2004) Large-sample learning of Bayesian networks is NP-hard. J Mach Learn Res 5:1287–1330
Chow CK, Liu CN (1968) Approximating discrete probability distributions with dependence trees. IEEE Trans Inf Theory 14(3):462–467
Cooper GF (1990) The computational complexity of probabilistic inference using Bayesian belief networks. Artif Intell 42(2–3):393–405
Cowell RG, Dawid P, Lauritzen, SL, Spiegelhalter, DJ (1999) Probabilistic networks and expert systems. Springer, New York, NY
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc -Ser B 39(1):1–38
Domingos P, Pazzani M (1997) On the optimality of the simple Bayesian classifier under zero-one loss. Mach Learn 29(2–3):103–130
Efron B (2005) Bayesians, frequentists, and scientists. J Am Stat Assoc 100(469):1–5
Friedman N, Geiger D, Goldszmidt M (1997) Bayesian network classifiers. Mach Learn 29(2–3):131–163
Friedman N, Goldszmidt M (1996) Learning Bayesian networks with local structure. In: Proceedings of the 12th annual conference on uncertainty in artificial intelligence (UAI), Portland, OR, pp 252–262
Grossman D, Domingos P (2004) Learning Bayesian network classifiers by maximizing conditional likelihood. In: Proceedings of the 21st international conference on machine learning (ICML), Banff, Canada, pp 46–53
Heckerman D (1998) A tutorial on learning with Bayesian networks. In: Jordan MI (ed) Learning in graphical models. Kluwer, Dordrecht, Netherlands, pp 301–354
Jensen FV (1997) An introduction to Bayesian networks. Springer, New York, NY
Kohavi R (1996) Scaling up the accuracy of naive-Bayes classifiers: a decision-tree hybrid. In: Proceedings of the 2nd international conference on knowledge discovery and data mining (KDD), Portland, OR, pp 202–207
Kononenko I (1991) Semi-naive Bayesian classifier. In: Proceedings of the 6th European working session on learning (EWSL), Porto, Portugal, pp 206–219
Lewis DD (1991) Naive (Bayes) at forty: the independence assumption in information retrieval. In: Proceedings of the 10th European conference on machine learning (ECML), Chemnitz, Germany, pp 4–15
McCallum A, Nigam K (1998) A comparison of event models for naive Bayes text classification. In: Working notes of the AAAI’98 workshop on learning for text categorization, Madison, WI, pp 4–15
McLachlan G, Krishnan T (2008) The EM algorithm and extensions, 2nd edn. Wiley, Hoboken, NJ
Ng AY, Jordan MI (2002) On discriminative versus generative classifiers: a comparison of logistic regression and naive Bayes. In: Dietterich TG, Becker S, Ghahramani Z (eds), Advances in neural information processing systems 14 (NIPS), pp 841–848. MIT Press, Cambridge, MA
Pearl J (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmanns, San Francisco, CA
Sahami M (1996) Learning limited dependence Bayesian classifiers. In: Proceedings of the 2nd international conference on knowledge discovery and data mining (KDD), Portland, OR, pp 335–338
Samaniego FJ (2010) A comparison of the Bayesian and frequentist approaches to estimation. Springer, New York, NY
Webb G, Boughton J, Wang Z (2005) Not so naive Bayes: aggregating one-dependence estimators. Mach Learn 58(1):5–24
Wu CFJ (1983) On the convergence properties of the EM algorithm. Ann Stat 11(1):95–103
Wu X, Kumar V, Quinlan JR, Ghosh J, Yang Q, Motoda H, McLachlan GJ, Ng A, Liu B, Yu PS, Zhou Z-H, Steinbach M, Hand DJ, Steinberg D (2007) Top 10 algorithms in data mining. Knowl Inf Syst 14(1):1–37
Zhang H (2004) The optimality of naive Bayes. In: Proceedings of the 17th international Florida artificial intelligence research society conference (FLAIRS), Miami, FL, pp 562–567
Zheng Z, Webb GI (2000) Lazy learning of Bayesian rules. Mach Learn 41(1):53–84
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Zhou, ZH. (2021). Bayes Classifiers. In: Machine Learning. Springer, Singapore. https://doi.org/10.1007/978-981-15-1967-3_7
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DOI: https://doi.org/10.1007/978-981-15-1967-3_7
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