C. Thornton. Parity: the problem that won't go away. In G. McCalla, editor, Advance in Artificial Intelligence, pages 362--374. Springer, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....n;0 ) to r. This analysis provides evidence that PI models should not be rare in real world domains. In the following, we provide more evidence by analyzing two special cases of PI models. It is well known that parity problems cause difficulty to many machine learning algorithms, see for example [4, 3, 6]. A parity problem can be described as follows: A set of marginally independent input variables fX 1 ; X n Gamma1 g each take the value 0 or 1 with an equal chance. An output variable X n takes 0 or 1 such that the total number of 1 s is even (for even parity) The following proposition shows ....

....the other input variables in a parity problem is unnecessary. Once the n variables behave according to a particular parity, we would not be able to tell which one is the output variable since each variable has the same marginals and each may assume the role of the output. Recently, it was shown [6] that parity problems are special cases of modulus addition problems. The latter display similar properties of parity problems and cause difficulty to ID3 like algorithms. A modulus addition problem can be described as follows: A problem domain consists of a set of marginally independent and ....

C. Thornton. Parity: the problem that won't go away. In G. McCalla, editor, Advance in Artificial Intelligence, pages 362--374. Springer, 1996.

....increase as r grows is apparently delayed until r gets close to 50 . We note the use of more refined partitions over the instance space alleviates the effects of the fragmentation problem but does not eliminate it (Sect. 4) as evidenced by the results on parity concepts PAR9a and PAR12a (see [25]) where the advantage for DALIrules is significant. None of the real world domains may achieve this high r, where no significant difference is observed between these two systems. Figures 7a and 7b depict regression lines for the differences on predictive accuracy between DALIrules and DALI . An ....

Thornton C.: Parity: The Problem that Won't Go Away. In Proceedings of the 11th Biennial Conference of the Canadian Society for Computational Studies of Intelligence, Toronto Ontario, Canada, (1996) 362--374

....researchers. Its definition is simple (determine whether there is an odd or even number of 1 s in an n length bit string of 1 s and 0 s) but established state of the art algorithms such as C4.5 [10] and backpropagation [6] cannot learn it even with small n, i.e. backpropagation fails with n 4 [11]. That is, these algorithms are unable to generalize from learning instances of a parity n task to unseen new instances of the same task. As with date calculation, this is due to the statistical neutrality of the task. The solution of the problem must lie in having some comprehensive overview over ....

....(The average error of 6. 2 made by bp som stems from a single experiment out of the ten performing at chance level, and the remaining nine yielding about 1 error) bp som is able to learn the parity 12 task quite accurately; bp and bpwd fail relatively, which is consistent with other findings [11]. As an additional analysis, we have investigated the differences in hidden unit activations after training with the three learning algorithms. To visualize the differences between the representations developed at the hidden layers of the mfns trained with bp, bpwd, and bp som, we also trained ....

Thornton, C. (1996). Parity: the problem that won't go away. In G. McCalla (Ed.), Proceeding of AI-96, Toronto, Canada (pp. 362-374). Berlin: Springer Verlag.

....algorithms) is unjustified. We discuss below some special PI models which provide further evidence for the existence of PI models in practice. 7 Special PI models 7. 1 Parity problems It is well known that parity problems cause failure for many machine learning algorithms, see for example [21, 13, 26]. A parity problem can be described as follows: A set of marginally independent input variables fX 1 ; X n Gamma1 g each take the value 0 or 1 with an equal chance. An output variable X n takes 0 or 1 such that the total number of 1 s is even (for even parity) The following proposition ....

....a parity problem is unnecessary. Once the n variables behave according to a particular parity, we would not be able to tell which one is the output variable since each variable has the same marginals and each may assume the role of the output. 7. 2 Modulus addition problems Recently, it was shown [26] that parity problems are special cases of modulus addition problems. The latter display similar properties of parity problems and cause failure of ID3 like algorithms. A modulus addition problem can be described as follows: A problem domain consists of a set of marginally independent and ....

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C. Thornton. Parity: the problem that won't go away. In G. McCalla, editor, Advance in Artificial Intelligence, pages 362--374. Springer, 1996.

.... well known capabilities with respect to the XOR problem being offered as a proof [19] However, this demonstration is open to re interpretation [24] and a conservative judgement on this issue would now rate the abilities of the MLP with respect to relational problems as still under evaluation [25]. Similar remarks might be made with respect to the SVM, at least in the configuration used for this experiment (i.e. using the standard polynomial kernel function) However, the fact that the performance achieved by the SVM on these data is close to that achieved by the ineluctably ....

Thornton, C. (1996). Parity: the problem that won't go away. In G. McCalla (Ed.), Proceeding of AI-96 (Toronto, Canada) (pp. 362-374). Springer. 15

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Thornton, C. (1996b). Parity: the problem that won't go away. In G. McCalla (Ed.), Proceeding of AI-96 (Toronto, Canada) (pp. 362-374). Springer.

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