Kononenko, I. (1991). Semi-naive bayesian classifier. European Working Session on Learning-EWSL91. Lecture Notes in Computer Science, 482:206--219.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[8] has become one of the most popular techniques in solving this type of problems. By relaxing the strong assumption, i.e. the independency among the data attributes, of NB, many researchers have developed other types of Bayesian belief networks. Among them are Semi naive Bayesian network [5], Selective naive Bayesiannetwork [6] and Tree Augmented Naive Bayesian network [4] Moreover, although the Chow Liu tree (CLT) 3] was early proposed in 1968, it can also be regarded as a type of Bayesian belief network with a looser assumption than NB. CLT is shown to be a competitive method ....

I. Kononenko. Semi-naive bayesian classifier. In Proceedings of sixth European Working Session on Learning, pages 206--219. Springer-Verlag, 1991.

....features be dependent on it, i.e. will it be useful to the network While our complex functions may be any binary function, traditionally only binary functions that can be represented using the And operator are usually considered. Previously, And functions have been used in naive Bayes networks [43, 59]. Within this chapter, we will describe several methods for adding complex feature functions. A 61 couple of these methods will only apply to the RLN since the magnitude of the weights between functions is used. Two methods, which use variable frequency and average error, can be applied to both ....

I. Kononenko. Semi-naive bayesian classifier. In Y. Kodrato#, editor, Proceedings of the European Working Session on Learning : Machine Learning (EWSL-91), volume 482 of LNAI, pages 206--219, Porto, Portugal, March 1991. Springer Verlag.

.... Interaction gain is identical to the notion of mutual information among three random variables [3] 4 Detecting and Resolving Interactions A number of methods have been proposed to account for dependencies in machine learning, in particular with respect to the nave Bayesian classification model [4 6], showing improvement in comparison with the basic model. The first two of these methods, in a sense, perform feature construction; new features are constructed from interacting attributes, by relying on detection of interactions. On the other hand, tree augmentation [6] merely makes the ....

Kononenko, I.: Semi-naive Bayesian classifier. In Kodrato#, Y., ed.: European Working Session on Learning - EWSL91. Volume 482 of LNAI., Springer Verlag (1991)

....stepwise diagnostic process. Note that each box may contain different ML algorithm. In our experiments we used the following well known Machine Learning methods, which are all able to give both categorical and probabilistic classifications. naive Bayesian classifier (also called idiot Bayes) [3] decision trees (Assistant I) 4] multilayered feedforward neural networks with backpropagation learning [11] 5 Experimental results We performed our experiments on the IHD dataset of 327 patients (Table 1) Pretest probabilities were estimated from the signs and symptoms, then exercise ....

I. Kononenko. Semi-naive Bayesian classifier. In Y. Kodratoff, editor, Proc. European Working Session on Learning-91, pages 206--219, Porto, Potrugal, 1991. Springer-Verlag.

....CAD study [10, 19] was rationalization of 607 existing clinical procedure for the third diagnostic step (myocardial scintigraphy) 608 hopefully increasing the specificity while not decreasing the sensitivity . 609 4 Results 610 We performed all our experiments by using naive Bayesian classifier [13] as our 611 Machine Learning tool of choice, since it usually performs very well in medi 612 cal problems and can comprehensibly explain its classifications to the physicians. 613 However, this does not mean that our approach is limited to this Machine Learning 614 paradigm. In fact, many ....

I. Kononenko. Semi-naive Bayesian classifier. In Y. Kodratoff, editor, Proc. Eu- 797 ropean Working Session on Learning-91, pages 206--219, Porto, Potrugal, 1991. 798 Springer-Verlag. 799

....on the basis of medical (anatomical, physiological) taxonomy; this seems not to correspond to attribute interactions, as we have defined them in this text. 4 Construction of Classification Models While the naive Bayesian classifiers cannot exploit the information hidden in a positive interaction [9, 10], the attributes in negative interactions tend to confuse their predictions [11] The e#ects of negative interactions have not been studied extensively, but provide explanation for benefits of feature selection procedures, which are one way of eliminating this problem. With resolving ....

Kononenko, I.: Semi-naive Bayesian classifier. In Kodrato#, Y., ed.: European Working Session on Learning - EWSL91. Volume 482 of LNAI., Springer Verlag (1991)

....Furthermore, so called Semi Naive Bayesian networks are proposed to remedy violations of NB s assumption by joining attributes into several combined attributes based on a conditional independency assumption among the combined attributes. Some performance improvements have been demonstrated in [17] [25] Figure 2 is a graphical illustration of Semi Naive Bayesian network. At this time, the conditional independency occurs among the combined attributes . However, even SNB makes the constraint of NB looser, such a relaxation is slight. SNB is still strongly restrained for its conditional ....

....parameters of each component. This optimization algorithm with a global nature will guarantee the maximization step in EM and then guarantee the objective function will increase iteratively. In this way, the iterative EM process can go to a convergence point. However traditional algorithms of SNB [17] [25] often search their structures based on some heuristic methods, for the reason of large search space of SNB. While these heuristic approaches decrease the total time cost, they bring in a local nature as well, which will prevent them into the mixture structure. In this paper, we firstly ....

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I. Kononenko. Semi-naive bayesian classifier. In Proceedings of sixth European Working Session on Learning, pages 206--219. SpringerVerlag, 1991.

....network has become one of the most popular techniques in solving this type of problems. By relaxing the strong assumption, i.e. the independency among the data attributes, of NB, many researchers have developed other types of Bayesian belief networks. Among them are Semi naive Bayesian network [5], Selective naive Bayesiannetwork [6] and Tree Augmented Naive Bayesian network [4] Moreover, although the Chow Liu tree (CLT) 3, 9] was early proposed in 1968, it can also be regarded as a type of Bayesian belief network with a looser assumption than NB. CLT is shown to be a competitive ....

I. Kononenko. Semi-naive bayesian classifier. In Proceedings of sixth European Working Session on Learning, pages 206--219. Springer-Verlag, 1991.

....Bayesian networks as classifiers. Since the strict assumption in NB can be violated strongly in many cases, researchers have wondered if the performance will be better when the strong independence assumption between variables in NB is relaxed. Then the so called semi naive Bayesian network(SNB) [5] [13] was invented. SNB constrains the network s structure by dividing the variables into several sets based on some criterions. Inside each set, the variables are assumed dependent while inter sets are independent, given the class label. Also other classifiers such as K2 [8] TANB [3] were ....

....complex SNB structure and then we try to find the optimal structure in this restriction. One interesting observation is that our proposed SNB has a polynomial time cost in searching a suboptimal structure. We do not need a great number of iterations on the training dataset as in traditional SNB [5]. Also we do not just combine pairs of attributes as in [13] since in our approach we can combine any number of variables fewer than a bound. At the same time, in [5] there is no evidence that shows a sub optimal or optimal structure can be maintained while our approach is shown to be suboptimal ....

[Article contains additional citation context not shown here]

I. Kononenko, "Semi-naive Bayesian classifier', Proceedings of sixth European Working Session on Learning, Springer-Verlag, pp. 206-219, 1991.

....the target attribute, given the values of the input attributes in each subset. Mathematically it can be formulated as follows: k=1 P I(S;G k ) y=vy;j ja i =xq;i i2Rk ) P I(S;G k ) y=vy;j ) 1 In fact extending the Naive Bayesian classifier by joining attributes is not new. Kononenko [21] have suggested the Semi Naive Bayesian Classifier that use a conditional independence test to join attributes. Domingos and Pazzani [10] used estimated accuracy (as determined by leaveoneout cross validation on the training set) In both cases, the suggested algorithm finds the single best pair ....

Kononenko, I., "Seminaive Bayesian classifier," in Proceedings of the Sixth European Working Session on Learning, SpringerVerlag, pp. 206-219, 1991.

....i in an observation q. V y represents the domain of the target attribute. R k denotes the indexes of the attributes that belong to subset k. y represents the class variable or the target attribute. In fact extending the simple Bayesian classifier by join ing attributes is not new. Kononenko [11] used a conditional independence test to join attributes. Domingos and Pazzani [4] used estimated accuracy (as determined by leave one out cross validation on the training set) In both cases, the suggested algorithm finds the single best pair of attributes to join by considering all possible ....

I. Kononenko. Semi-naive bayesian classifier. Proceedings of the Sixth European Working Session on Learning, pages 206--219, 1991.

....of the Naive Bayesian classifier. While we discussed those algorithms most closely related to KDB in Section 8.3 to more clearly contrast them with our work, we present other (different) methods here. One of the earliest such attempts is Kononenko s work on Semi Naive Bayesian classifiers [96] which considered creating new features from pairs of existing features as a means of relaxing the strict independence assumption. Unfortunately, this method was not capable of realizing any empirical accuracy improvements over Naive Bayes. Similarly, Pazzani [124] has looked at constructive ....

Kononenko, I. Semi-naive bayesian classifier. In Proceedings of the Sixth European Working Session on Learning (1991), Pitman, pp. 206--219.

....[102] clinical gait analysis [77] and analysis of molecular similarity [9] 47 4. 3 Bayesian classifier The Bayesian classifier uses the naive Bayesian formula to calculate the probability of each class c j given the values v i k of all the attributes for a given instance to be classified [81, 82]. For simplicity, let (v 1 . v n ) denote the n tuple of values of example e k to be classified. Assuming the conditional independence of the attributes given the class, i.e. assuming p(v 1 . v n c j ) # i p(v i c j ) then p(c j v 1 . v n ) is calculated as follows: p(c j v 1 . v ....

..... v n ) is proportional to: p(c j ) # i p(c j v i ) p(c j ) 5) Di#erent probability estimates can be used for computing the probabilities (e.g. the relative frequency, the Laplace estimate, the m estimate) Instead of the simple relative frequency estimate, computed as N(c j ) Nex , [81, 82] use the Laplace law of succession for computing the prior probability [119] p(c j ) N(c j ) 1 N ex N cl (6) where N ex is the number of examples, N cl the number of classes, and N(c j ) the number of examples of class c j . For computing the estimate of conditional probabilities [81, ....

[Article contains additional citation context not shown here]

Kononenko, I., "Semi-naive Bayesian classifier." In: Proc. European Working Session on Learning-91 (Kodrato#, Y., ed.), Porto, Springer, 1991, pp. 206-219. 56

....Furthermore, it has been shown to be optimal under zero one loss in a larger subspace [6] Given these facts, 3 the general idea is that if we somehow relax the assumptions that are made and keep the way of reasoning , we can get a more accurate classifier. This has been tried in different ways [9, 13, 14, 15, 18, 21]. From our point of view TAN are the more coherent and best performing enhancement to Naive Bayes up to now. In this section we discuss the TAN induction algorithm presented at [9] After that we apply the multinomial sampling approach to the TAN induction problem and get a maximum likelihood TAN ....

I. Kononenko. Semi-naive bayesian classifier. In Y. Kodratoff, editor, Proc. Sixth European Working Session on Learning, pages 206--219. Berlin: Springer-Verlang, 1991.

....In the first case, the class post test probability is equal to its prior probability, whereas in the second case it is 0. 4 Experiments To validate our proposed methodology we performed extensive experiments with 6 different Machine Learning algorithms naive and semi naive Bayesian classifier[7], backpropagation neural network [13] K nearest neighbour, locally naive Bayesian classifier (a combination KNN and naive Bayesian classifier) 8] Assistant (decision trees) 6] on 14 well known benchmark datasets (Tab. 1a and 1b) Table 1. Experimental results with transductive reliability ....

I. Kononenko. Semi-naive Bayesian classifier. In Y. Kodratoff, editor, Proc. European Working Session on Learning-91, pages 206--219, Porto, Potrugal, 1991. Springer-Verlag.

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Kononenko, I. (1991). Semi-naive bayesian classifier. European Working Session on Learning-EWSL91. Lecture Notes in Computer Science, 482:206--219.

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I. Kononenko, "Semi-naive Bayesian Classifier," 6th European Working Session on Learning, pp. 206-219, 1991.

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I. Kononenko, "Semi-naive Bayesian Classifier," 6th European Working Session on Learning, pp. 206-219, 1991. 103

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I. Kononenko. Semi-naive Bayesian classifier. In Y. Kodratoff, editor, Proc. European Working Session on Learning-91, pages 206--219, Porto, Potrugal, 1991. Springer-Verlag.

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Kononenko, I.: Semi-Naive Bayesian Classifier. In: Proceedings of European Conference on Artificial Intelligence, (1991) 206-219

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I. Kononenko, "Semi-Naive Bayesian Classifier", In Proceedings of the sixth European Working Session on Learning, 206-219, 1991.

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I. Kononenko. Semi-naive bayesian classifier. In Proceedings of sixth European Working Session on Learning, pages 206--219. Springer-Verlag, 1991.

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I. Kononenko. Semi-naive Bayesian classifier. In ECAI91, pages 206--219, 1991.

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Kononenko, I. (1991). Semi-naive Bayesian classifier. In Proceedings of the 6 th European Working Session on Learning, 206-219. Berlin: Springer- Verlag.

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