D. H. Wolpert. A mathematical theory of generalization. Complex Systems, 4:151--200, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....from minimizing an error function. The ANN with the minimum error does not necessarily mean that it has best generalization unless there is an equivalence between generalization and the error function. Unfortunately, measuring generalization exactly and accurately is almost impossible in practice [15], although there are many theories and criteria on generalization, such as the minimum description length (MDL) 16] Akaike information criteria (AIC) 17] and minimum message length (MML) 18] In practice, these criteria are often used to define better error functions in the hope that ....

....The nature of the problem is unchanged. Similar situations occur with other machine learning methods, where an error function has to be defined. A learning algorithm then tries to minimize the function. However, no error functions can guarantee that they correspond to the true generalization [15]. This is a problem faced by most inductive learning methods. There is no way in practice one can get around this except for using a good empirical function which might not correspond to the true generalization. Hence, formulating learning as optimization in this situation is justified. ....

D. H. Wolpert, "A mathematical theory of generalization," Complex Syst., vol. 4, pp. 151--249, 1990.

....training data set. The ANN with the minimum error on a training data set may not have best generalization unless there is an equivalence between generalization and the error on the training data. Unfortunately, measuring generalization quantitatively and accurately is almost impossible in practice [298] although there are many theories and criteria on generalization, such as the minimum description length (MDL) 299] Akaike information criteria (AIC) 300] and minimum message length (MML) 301] In practice, these criteria are often used to define better error functions in the hope that ....

D. H. Wolpert, "A mathematical theory of generalization," Complex Syst., vol. 4, no. 2, pp. 151--249, 1990.

....A test set, consisting of patterns previously unseen by the classifier, is then used to determine the classification performance. This ability to meaningfully respond to novel patterns, or generalize, is an important aspect of a classifier system and in essence, the true gauge of performance [1, 2]. Given infinite training data, consistent classifiers approximate the Bayesian decision boundaries to arbitrary precision, therefore providing similar generalizations [3] However, often only a limited portion of the pattern space is available or observable [4, 5] Given a finite and noisy data ....

D. H. Wolpert. A mathematical theory of generalization. Complex Systems, 4:151--200, 1990.

....A test set, consisting of patterns not previously seen by the classifier, is then used to determine the classification performance. This ability to meaningfully respond to novel patterns, or generalize, is an important aspect of a classifier system and in essence, the true gauge of performance [26, 48]. Given infinite training data, consistent classifiers approximate the Bayesian decision boundaries to arbitrary precision, therefore providing similar generalizations [14] However, often only a limited portion of the pattern space is available or observable [11, 12] Given a finite and noisy ....

D. H. Wolpert. A mathematical theory of generalization. Complex Systems, 4:151--200, 1990.

....A test set, consisting of patterns not previously seen by the classifier, is then used to determine the classification performance. This ability to meaningfully respond to novel patterns, or generalize, is an important aspect of a classifier system and in essence, the true gauge of performance [1, 2]. Given infinite training data, consistent classifiers approximate the Bayesian decision boundaries to arbitrary precision, therefore providing similar generalizations [3] However, often only a limited portion of the pattern space is available or observable [4, 5] Given a finite and noisy data ....

D. H. Wolpert. A mathematical theory of generalization. Complex Systems, 4:151--200, 1990.

....training data set. The ANN with the minimum error on a training data set may not have best generalization unless there is an equivalence between generalization and the error on the training data. Unfortunately, measuring generalization quantitatively and accurately is almost impossible in practice [298] although there are many theories and criteria on generalization, such as the minimum description length (MDL) 299] Akaike information criteria (AIC) 300] and minimum message length (MML) 301] In practice, these criteria are often used to define better error functions in the hope that ....

D. H. Wolpert, "A mathematical theory of generalization," Complex Systems, vol. 4, no. 2, pp. 151--249, 1990.

....from minimising an error function. The ANN with the minimum error does not necessarily mean that it has best generalisation unless there is an equivalence between generalisation and the error function. Unfortunately, measuring generalisation exactly and accurately is almost impossible in practice [15], although there are many theories and criteria on generalisation, such as the minimum description length (MDL) 16] Akaike information criteria (AIC) 17] and minimum message length (MML) 18] In practice, these criteria are often used to define better error functions in the hope that ....

....The nature of the problem is unchanged. Similar situations occur with other machine learning methods, where an error function has to be defined. A learning algorithm then tries to minimise the function. However, no error functions can guarantee that they correspond to the true generalisation [15]. This is a problem faced by most inductive learning methods. There is no way in practice one can get around this except for using a good empirical function which might not correspond to the true generalisation. Hence, formulating learning as optimisation in this situation is justified. ....

D. H. Wolpert, "A mathematical theory of generalization, " Complex Systems, vol. 4, pp. 151--249, 1990.

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D. H. Wolpert. A mathematical theory of generalization. Complex Systems, 4:151--200, 1990.

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D. H. Wolpert, "A mathematical theory of generalization," Complex Systems, vol. 4, pp. 151--249, 1990.

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David Wolpert. A mathematical theory of generalization, part II. Complex Systems, 4:201-- 249, 1990.

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David Wolpert. A mathematical theory of generalization, part I. Complex Systems, 4:151-- 200, 1990.

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Wolpert, D. H. (1990). A Mathematical Theory of Generalization. Complex Systems 4: 151249.

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D. H. Wolpert. A mathematical theory of generalization. Complex Systems, 4:151--249, 1990.

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D. H. Wolpert, "A mathematical theory of generalization," Complex Systems, vol. 4, pp. 151--249, 1990.

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D. H. Wolpert, "A mathematical theory of generalization, " Complex Systems, vol. 4, pp. 151--249, 1990.

No context found.

D. H. Wolpert. A mathematical theory of generalization. Complex Systems, 4:151--249, 1990.

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