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On the Use of Naive Bayesian Classifiers for Detecting Elementary and Coordinated Attacks

Kenaza T., Tabia K., Benferhat S.

Fundamenta Informaticae

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2011

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Vol. 105, nr 4

435-466

EN

Bayesian networks are very powerful tools for knowledge representation and reasoning under uncertainty. This paper shows the applicability of naive Bayesian classifiers to two major problems in intrusion detection: the detection of elementary attacks and the detection of coordinated ones. We propose two models starting with stating the problems and defining the variables necessary for model building using naive Bayesian networks. In addition to the fact that the construction of such models is simple and efficient, the performance of naive Bayesian networks on a representative data is competing with the most efficient state of the art classification tools. We show how the decision rules used in naive Bayesian classifiers can be improved to detect new attacks and new anomalous activities. We experimentally show the effectiveness of these improvements on a recent Web-based traffic. Finally, we propose a naive Bayesian network-based approach especially designed to detect coordinated attacks and provide experimental results showing the effectiveness of this approach.

2

A Framework for Iterated Belief Revision Using Possibilistic Counterparts to Jeffrey's Rule

Benferhat S., Dubois D., Prade H., Williams M-A.

Fundamenta Informaticae

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2010

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Vol. 99, nr 2

147-168

EN

Intelligent agents require methods to revise their epistemic state as they acquire new information. Jeffrey’s rule, which extends conditioning to probabilistic inputs, is appropriate for revising probabilistic epistemic states when new information comes in the form of a partition of events with new probabilities and has priority over prior beliefs. This paper analyses the expressive power of two possibilistic counterparts to Jeffrey's rule for modeling belief revision in intelligent agents. We show that this rule can be used to recover several existing approaches proposed in knowledge base revision, such as adjustment, natural belief revision, drastic belief revision, and the revision of an epistemic state by another epistemic state. In addition, we also show that some recent forms of revision, called improvement operators, can also be recovered in our framework.

3

Making Revision Reversible: an Approach Based on Polynomials

Benferhat S., Dubois D., Lagrue S., Papini O.

Fundamenta Informaticae

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2002

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Vol. 53, nr 3,4

251-280

EN

This paper deals with iterated belief change and proposes a drastic revision rule that modifies a plausibility ordering of interpretations in such a way that any world where the input observation holds is more plausible that any world where it does not. This change rule makes sense in a dynamic context where observations are received, and the newer observations are considered more plausible than older ones. It is shown how to encode an epistemic state using polynomials equipped with the lexicographic ordering. This encoding makes it very easy to implement and iterate the revision rule using simple operations on these polynomials. Moreover, polynomials allow to keep track of the sequence of observations. Lastly, it is shown how to efficiently compute the revision rule at the syntactical level, when the epistemic state is concisely represented by a prioritized belief base. Our revision rule is the most drastic one can think of, in accordance with Darwiche and Pearl's principles, and thus contrasts with the minimal change rule called natural belief revision. The paper also shows how to obtain the reversibility of Boutilier's natural belief revision and possibilistic revision using polynomials.