Hi, Well Naive Bayesian classifier (NBC) assumes independence between all attributes given a class, which is seldom true. That is why it is called Naive. In contrast, in a Bayesian network (BN) you can make a more detailed (true) model of the problem using several layers of dependecies. However, NBC can actually be modelled as a simple form of NB. So there is actually not a clear cut difference between them, other than that NBC makes a very much simplified assumption. The question is rather whether a NBC is good enough to do the job, rather than whether which approach is best.

Tomas is right. A naive bayes calssifier will assume independence between different dimensions which may or may not be true depending on your problem. however, ti is much simpler to use. What you're referring to is the forgetting nature of a Markov chain , i.e. dependence only on the previous state. however, each state might be multidimensional, so the markov nature of the sequence does not have anything to do with modeling the state itself (at each point in the sequence or time) as naive or full blown bayes network.

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a good reminder of the quality of the "Naive Bayes" predictor

Idiot's Bayes: Not So Stupid after All?

David J. Hand and Keming Yu

International Statistical Review / Revue Internationale de Statistique

Vol. 69, No. 3 (Dec., 2001), pp. 385-398

http://venus.unive.it/romanaz/complstat/hand_naive_bayes.pdf

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i agree with Tomas and Vikas,

i also want to point that (Lowd & Domingos 2005) report, after extensive experiments on large set of data, that BN and Naïve Bayesian are similarly accurate when used for inference purposes. However, Naïve Bayes inference is significantly faster which make it more favorable in real-time domain.

furthermore, although the conditional independence assumption is obviously questionable, Naïve-Bayes has surprisingly outperformed many sophisticated classifiers over a large number of datasets (Langley et al. 1992).

Lowd, D. and Domingos, P. “Naive Bayes Models for Probability Estimation.” Proceedings of the 22ndInternational Conferenceon Machine Learning, August 7-11, Bonn, Germany, ACM 2005 Pages: 529 – 536, 2005.

Langley, P., Iba, W., and Thompson, K. “An analysis of Bayesian classifiers.” In Proceedings of theTenth National Conference on Artificial Intelligence, pages 223–228. AAAI Press and MIT Press,1992.

There is one more reason why an unrestricted Bayesian network (BN) may perform better.  In the case of a naive Bayes (NB) network, the class node does not have any parents.  Parents of the class node, which behave differently from its children (in terms of independence conditions), may offer a way of influencing the prior probability distribution over classes.

In theory a full BN should perform better but in practice, precisely because of the Markov blanket around the class node, when there are not too many missing vales, nodes around the class node may shield it from the influences of less important features. Less important does not mean worthless in terms of predicting the class.  I have seen cases in which simple NB networks performed better than BNs, even though they should have performed worse (for the reasons outlined by Tomas and Vikas above).

Although there are very good replays from the above experts, however., to my experience, the main benefits of Bayesian framework are:

1) Straightforward and easy.

2) Very fast.

3) Low storage space.

4) No initial guess.

5) Very less training data, for optimality., I.e., 10 to 20 % training data is sufficient.

6) Very good accuracy.