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J. Kalbfleish. Probability and Statistical Inference, volume II. Springer, New York, 1979.

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Ai Miei Genitori Ii - Acknowledgements First Would   (Correct)

....its expected accuracy is better than the default accuracy, given by the probability of the more frequent of the classes Phi and Psi. This probability is estimated from the entire training set by the relative frequency estimate. The significance test is based on the likelihood ratio statistic [Kal79] Given a clause C, the likelihood ratio of C is given by LikelihoodRatio(C) 2n(C) Theta p( PhijC) log p( PhijC) p a ( Phi) p( PhijC) log p( PsijC) p a ( Psi) where n(C) are the examples covered by C, n (C) of which are positive, p a ( Phi) and p a ( Psi) are the prior ....

....stopping criterion: mFOIL stops adding a clause to the theory when too few positive examples remain for a clause to be significant or when no significant clause can be found with expected accuracy greater than the default. The significance test is based on the likelihood ratio statistic [Kal79] a clause is deemed significant if its likelihood ratio is higher than a certain significance threshold. The default value for the significance threshold is 6.64 corresponding to a significance level of 99 . Unless otherwise specified, mFOIL was run in all the experiments with the parameters set ....

J. Kalbfleish. Probability and Statistical Inference, volume II. Springer, New York, 1979.


The CN2 Induction Algorithm - Clark, Niblett (1989)   (227 citations)  (Correct)

....result from random variation. The issue is whether the observed differences are too great to be accounted for purely by chance. If so, cn2 assumes that the complex reflects a genuine correlation between attributes and classes. To test significance, the system uses the likelihood ratio statistic [15]. This is given by 2 n X i=1 f i log(f i =e i ) where the distribution F = f 1 ; f n ) is the observed frequency distribution of examples among classes satisfying a given complex and E = e 1 ; e n ) is the expected frequency distribution of the same number of examples under the ....

J. Kalbfleish. Probability and Statistical Inference, volume 2. Springer-Verlag, NY, 1979.


Scalability Of Machine Learning Algorithms - Paliouras (1993)   (1 citation)  (Correct)

....(3. 18) where n is the number of classes, f i is the number of examples belonging to the i th class, in the set of examples covered by the complex and e i is the total number of examples belonging to the class, scaled to the coverage of the complex (i.e. P n i=1 f i ) The likelihood ratio [Kalbfleish, 1979], measures the significance, in terms of classification, of the complex, based on the distance between the resulting class distribution and the default one. In order for the rule generation process to continue the result of this measure has to be above a user defined threshold, similar to the ....

Kalbfleish, J. Probability and Statistical Inference, volume 2. Springer-Verlag, New York, 1979.


Abductive Concept Learning - Kakas, Riguzzi (1999)   (2 citations)  (Correct)

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) J. Kalbfleish. Probability and Statistical Inference, volume II. Springer, New York, 1979.

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