Thorsten Joachims. Estimating the generalization performance of a SVM efficiently. In Pat Langley, editor, Proceedings of the International Conference on Machine Learning, pages 431--438, San Francisco, CA, USA, 2000. Morgan Kaufman.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....machines, or SVMs, are learning machines that plot the training vectors in highdimensional feature space, labeling each vector by its class. SVMs classify data by determining a set of support vectors, which are members of the set of training inputs that outline a hyper plane in the feature space [13,14]. SVMs provide a generic mechanism to fit the surface of the hyper plane to the data through the use of a kemel function. The user may provide a function (e.g. linear, polynomial, or sigrnoid) to the SVMs during the training process, which selects support vectors along the surface of this ....

Joachims T. (2000) "Estimating the Generalization Performance of a SVM Efficiently," Proceedings of the International Conference on Machine Learning, Morgan Kaufman.

....error of a decision rule. However, it is computationally too expensive to perform iteratively in our framework. Estimating the SVM generalization performance has been researched actively based on a strong theoretical foundation. One of the most recent methods, estima tion of leave one out errors [13], has shown to be effi cient and fairly accurate. We used this method in our experiments. Given the generated SVM model of d degree polynomial kernel, Steps 3 to 5 extracts the most compact subsets of feature combinations that generates higher classification accuracy than the user threshold 0 as ....

T. Joachims. Estimating the generalization per- formance of a SVM efficiently. In P. Langley, editor, Proceedings of ICML-00, 17th International Conference on Machine Learning, pages 431-438, Stanford, US, 2000. Morgan Kaufmann Publishers, San Francisco, US.

....in the proceeding sec Though it would be possible to find optimal parameters automatically by cross evaluation, this would increase the respond time of the system making interactive work quite unpleasant. This is true even if the efficient performance estimators for the SVM presented in [7] are used. tion. Secondly it is based on the context in which objects appear. The idea is the following: If two objects appear together in many user edited clusters, then we can assume, that these objects are in some way similar. This is a very interesting feature of our system, as items are not ....

T. Joachims. Estimating the generalization performance of a SVM efficiently. In P. Langley, editor, Proceedings of ICML-00, 17th International Conference on Machine Learning, pages 431--438, Stanford, US, 2000. Morgan Kaufmann Publishers, San Francisco, US.

.... for the detection of each manner class. Sonorant frames were trained against all non sonorant frames including frication, silence, and stops. 30,000 frames of speech were selected for each class randomly from the TIMIT training data, from both male and female utterances. The Xi Alpha estimates [8,9] of the error bound provided by the learning process and the number of support vectors for each machine is shown in Table 4. We choose RBF kernel with g = 0.01 for speech segmentation experiments because of lowest error bound estimate of 10.86 . Similar analysis was carried out for other manner ....

T. Joachims, "Estimating the Generalization Performance of a SVM Efficiently", Proceedings of the International Conference on Machine Learning, Morgan Kaufman, 2000.

....criteria of stability of the result during the learning steps, improvement of the prediction accuracy during the progress of the training and recoverability from errors resulting of the drifting concepts. Another approach to the handling of drifting concepts has been pursued in [Klinkenberg and Joachims, 2000] where a performance estimator [Joachims, 2000] has been used to detect whether a drift in the underlying concept did occur, at which point the old data was being discarded and training took place only on the new data. This paper deals with the setting of incremental learning, i.e. the data is ....

....learning steps, improvement of the prediction accuracy during the progress of the training and recoverability from errors resulting of the drifting concepts. Another approach to the handling of drifting concepts has been pursued in [Klinkenberg and Joachims, 2000] where a performance estimator [Joachims, 2000] has been used to detect whether a drift in the underlying concept did occur, at which point the old data was being discarded and training took place only on the new data. This paper deals with the setting of incremental learning, i.e. the data is presented to the algorithm in several batches, ....

Joachims, T. (2000). Estimating the generalization performance of a SVM efficiently. In Proceedings of the International Conference on Machine Learning, San Francisco. Morgan Kaufman.

.... vectors to the generalization error of SVM via a bound on leave one out estimator [9] This result has been originally shown for a special case of classification with hard margin cost function (optimal hyperplane) The papers by Opper and Winther [10] Jaakkola and Haussler [6] and Joachims [7] extend Vapnik s result in the direction of bounds for classification error of SVM s. The first of those papers deals with the hard margin case, while the other two derive tighter bounds on classification error of the soft margin SVMs with ffl insensitive linear cost. In this paper we extend ....

T. Joachims. Estimating the Generalization Performance of an SVM Efficiently. In Proc. of the International Conference on Machine Learning, 2000. Morgan Kaufman.

....there exist some analytical expression of Leave One Out estimates of SVMs generalization error such as those recalled in [5] However, in order to use these estimates, one has to ensure that the margin optimization problem has been solved exactly. The same holds for Joachims e y estimators [10, 11]. This restriction prevents us from using these estimates as we only do a partial local optimization. To circumvent the problem, we propose to use the bound on generalization provided by a result of Cristianini and Shawe Taylor [7] for thresholded linear real valued functions. While the bound it ....

T. Joachims. Estimating the generalization performance of a svm efficiently. In Proc. of the Int. Conf. on Machine Learning. Morgan Kaufmann, 2000.

....there exist some analytical expression of Leave One Out estimates of SVMs generalization error such as those recalled in [6] However, in order to use these estimates, one has to ensure that the margin optimization problem has been solved exactly. The same holds for the xa estimators of Joachims [12, 14]. This restriction prevents from using these estimates as we only do a partial local optimization. To circumvent the problem, we use the bound on generalization provided by a result of Cristianini and Shawe Taylor [8] for thresholded linear real valued functions. The theorem follows: Theorem 1 ....

T. Joachims. Estimating the generalization performance of a svm efficiently. In Proc. of the 17 ICML. Morgan Kaufmann, 2000.

....classification in nontrivial cases. Our own work has focused on the extension of the Generalized Approximate Cross Validation (GACV) 35] 17] 8] from penalized likelihood estimates to SVM s, see [21] 20] 32] 29] At the Berkeley meeting, Bin Yu pointed GW to the ## method of Joachims [12], which turned out to be closely related to the GACV. Code for the ## estimate is available in SV M light http: ais.gmd.de thorsten svm light . At about this time there was a lot of activity in the development of tuning methods, and a number of them [26] 11] 22] 12] 2] turned out to be ....

....the ## method of Joachims [12] which turned out to be closely related to the GACV. Code for the ## estimate is available in SV M light http: ais.gmd.de thorsten svm light . At about this time there was a lot of activity in the development of tuning methods, and a number of them [26] 11] 22] [12] [2] turned out to be related under various circumstances. We first review optimal classification in the two category classification problem. We describe the standard case, where the training set is representative of the general population, and the cost of misclassification is the same for both ....

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T. Joachims.Estimating the generalization performance of an SVM efficiently.In Proceedings of the International Conference on Machine Learning, San Francisco, 2000. Morgan Kaufman.

....feedback, a filtering system should also be able to achieve a good performance, even if only few labeled training examples are provided. This paper proposes a method for detecting and handling concept changes with support vector machines extending the approach described in [Klinkenberg and Joachims, 2000] by using unlabeled data to reduce the need for labeled data. The approach has a clear theoretical motivation and does not require complicated parameter tuning. After reviewing other work on adaptation to changing concepts and shortly describing inductive and transductive support vector machines, ....

....hyperlinks pointing to this page. Blum and Mitchell develop a boosting scheme which exploits a conditional independence between these representations. 4 Window Adjustment by Optimizing Performance The method proposed in this paper is an extension of the approach described in [Klinkenberg and Joachims, 2000] This approach to handling drift in the distribution of examples uses a window on the training data. This window should include only those (labeled) examples which are sufficiently close to the current target concept. Assuming the amount of drift increases with time, the window includes the ....

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T. Joachims. Estimating the generalization performance of a SVM efficiently. In Proceedings of the Seventeenth International Conference on Machine Learning, San Francisco, 2000. Morgan Kaufman.

.... by: X p 0 p S 2 p : It has been shown [20] that the span S p is bounded by the diameter of the smallest sphere enclosing the training points and since P 0 p = 1= 2 , we nally get T 4 R 2 2 : A similar derivation as the one used in the span bound has been proposed in [10], where the leave one out error is bounded by jfp; 2 0 p R 2 y p f 0 (x p )gj, with 0 K(x i ; x i ) R 2 ; 8i. Link with Opper Winther When the support vectors do not change, the hard margin case without threshold gives the same value as the Opper Winther bound, namely: S 2 p = ....

T. Joachims. Estimating the generalization performance of a svm ef- ciently. In Proceedings of the International Conference on Machine Learning. Morgan Kaufman, 2000.

....also been proposed by Scholkopf et al. [32] which leads to an algorithm which has performed well in practice for a small number of datasets. The most economical way to use the training data is to use a leave one out procedure [3,13] As an example, we consider a recent scheme proposed by Joachims [14]. In this approach the number of leave one out errors of an L 1 norm soft margin SVM is bounded by jfi : 2ff i B 2 i ) 1gj=m where ff i are the solutions of the optimisation task in (10,6) and B 2 is an upper bound on K(x i ; x i ) with K(x i ; x j ) 0 (we can determine i from y i ( ....

....this quantity (the system is not retrained with datapoints left out: the bound is determined using the ff 0 i from the solution of (10,6) The kernel parameter is then incremented or decremented in the direction needed to lower the bound. This method has worked wekk on classification of text [14]. 6 Further techniques based on kernel representations. So far we have considered methods based on linear and quadratic programming. Here we shall consider further approaches which may utilise general nonlinear programming or other techniques. In particular, we will consider approaches to two ....

T. Joachims, Estimating the Generalization Performance of an SVM efficiently. Proceedings of the Seventeenth International Conference on Machine Learning. Morgan Kaufmann, 2000. p. 431-438.

....to selecting an appropriate window size that does not involve complicated parameterization. They key idea is to select the window size so that the estimated generalization error on new examples is minimized. To get an estimate of the generalization error we use a special form of ff estimates (Joachims, 2000). ff estimates are a particularly efficient method for estimating the performance of a SVM. 4.1 ff Estimators ff estimators are based on the idea of leave one out estimation (Lunts Brailovskiy, 1967) The leaveone out estimator of the error rate proceeds as follows. From the training sample S ....

.... x 0 ) d = jfi : ff i R 2 Delta i ) 1gj (9) counts the number of training examples, for which the quantity ff i R 2 Delta i exceeds one. Since the document vectors are normalized to unit length in the experiments described in this paper, here R 2 Delta = 1. It is proven in Joachims (2000) that d is an approximate upper bound on the number of leave one out errors in the training set. With n as the total number of training examples, the ff estimators of the error rate is Err n ff (h L ) jfi : ff i R 2 Delta i ) 1gj n (10) The theoretical properties of this ....

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Joachims, T. (2000). Estimating the generalization performance of a SVM efficiently. Proceedings of the Seventeenth International Conference on Machine Learning. San Francisco: Morgan Kaufman.

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Thorsten Joachims. Estimating the generalization performance of a SVM efficiently. In Pat Langley, editor, Proceedings of the International Conference on Machine Learning, pages 431--438, San Francisco, CA, USA, 2000. Morgan Kaufman.

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Thorsten Joachims. Estimating the generalization performance of a SVM ef- ciently. In Pat Langley, editor, Proceedings of the Seventeenth International Conference on Machine Learning (ICML-2000), pages 431-438, San Francisco, CA, USA, 2000. Morgan Kaufmann.

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Thorsten Joachims, "Estimating the generalization performance of a SVM efficiently," in Proceedings of the International Conference on Machine Learning, Pat Langley, Ed., San Francisco, 2000, pp. 431--438, Morgan Kaufman.

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T. Joachims. Estimating the Generalization performance of an SVM Efficiently. International Conference on Machine Learning (ICML), 2000.

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Joachims, T.: Estimating the generalization performance of a SVM efficiently. In Proceedings of the International Conference of Machine Learning, San Francisco. Morgan Kaufman, (2000)

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JOACHIMS T. (2000). Estimating the generalization performance of a SVM efficiently. In P. LANGLEY, Ed., Proceedings of ICML-00, 17th International Conference on Machine Learning, p. 431--438, Stanford, US: Morgan Kaufmann Publishers, San Francisco, US.

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Thorsten Joachims. Estimating the generalization performance of a SVM efficiently. In Pat Langley, editor, Proceedings of ICML-00, 17th International Conference on Machine Learning, pages 431--438, Stanford, US, 2000. Morgan Kaufmann Publishers, San Francisco, US.

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Joachims, T. (2000). Estimating the generalization performance of a SVM efficiently. Proceedings of the Seventeenth International Conference on Machine Learning (ICML-2000) (pp.

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Joachims, T.: Estimating the generalization performance of a SVM efficiently. In Proceedings of the International Conference of Machine Learning, San Francisco. Morgan Kaufman, (2000)

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Joachims, T. Estimating the generalization performance of a SVM efficiently. Proceedings of the 17th International Conference on Machine Learning, 431-438, 2000.

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Thorsten Joachims. Estimating the generalization performance of a SVM ef- ciently. In Pat Langley, editor, Proceedings of the Seventeenth International Conference on Machine Learning (ICML-2000), pages 431-438, San Francisco, CA, USA, 2000. Morgan Kaufmann.

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Joachims, T. Estimating the Generalization Performance of an SVM efficiently. In Proceedings of the 17th International Conference on Machine Learning, Morgan Kaufmann,. 431-438, 2000.

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Joachims T (2000) Estimating the Generalization Performance of a SVM Efficiently. Proceedings of the International Conference on Machine Learning, Morgan Kaufman.

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T. Joachims. Estimating the generalization performance of an SVM efficiently. In Proc. 17th International Conf. on Machine Learning, pages 431--438. Morgan Kaufmann, San Francisco, CA, 2000.

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