Freund, Yoav, H. Sebastion Seung, Eli Shamir, and Naftali Tishby. 1997. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....distance from the current class boundaries. To accelerate the learning process one can define a threshold value 0 0:25 for update and change a prototype only if ls(1 ls) The emergence of a window zone for the update of prototypes can also be exploited by active learning strategies [16], 17] 18] Only data points which fall into the window region must be labelled. IV. NUMERICAL EXPERIMENTS FOR TOY EXAMPLES We first consider two simple one dimensional classification problems (Fig. 3) In problem no. 1 (Fig. 3 a) datapoints are drawn independently and identically distributed ....

Y. Freund, H. S. Seung, E. Shamir, and N. Tishby, "Selective Sampling Using the Query by Committee Algorithm," in Machine Learning, Vol. 28, pp. 133-168, 1997.

....crude, it still achieves considerable gains over the most probable display update strategy. C. Related Work The general idea of maximizing the expected information from a query has also been pursued in the machine learning literature under the name Active Learning or Learning with Queries [43]. Active learning techniques have been shown to outperform simple probability ranking for document classification [44] We know of no application of active learning techniques to database retrieval. Comparison searching with errors has also been studied in the theoretical computer science ....

Y. Freund, H. S. Seung, E. Shamir, and N. Tishby, "Selective sampling using the query by committee algorithm," in Advances in Neural Information Processing Systems, Cambridge, MA, 1993, MIT Press.

....function by using a novel method of interactively discovering challenging training pairs. Our key insight is to simultaneously build several redundant functions and exploit the disagreement amongst them to discover new kinds inconsistencies amongst duplicates in the dataset. Active learning [6, 8] methods also rely on a similar insight for selecting instances for labeling from a large pool of unlabeled instances. Unlike an ordinary learner that trains using a static training set, an active learner actively picks subsets of instances which when labeled will provide the highest information ....

....in confusion was the largest. Instances whose prediction the learner can already make with strong confidence will likely not have much e#ect on the learner. Theoretical justification for approximating expected reduction in confusion (formally, version space) with prediction uncertainty appear in [30, 1, 8]. The example above was for a simple case where the two classes are completely separable by the classifier. Reallife data is noisy and when picking instances based on uncertainty we need to make sure that we are not picking erroneous or outlying instances. We are more likely to gain from ....

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28(2-3):133--168, 1997.

....once annotated, giving the maximum information or knowledge gain to the system is selected. In machine learning literature, the idea of maximizing the expected information from a query has been studied under the name active 1520 9210 02 17.00 2002 IEEE learning or learning with queries [12]. It was revisited by Cox et al. when they updated the display of the query result in [8] We will present a more detailed survey of the active learning literature in Section II B. The key assumption we make throughout this paper is that, although the low level feature space cannot describe the ....

Y. Freund, H. S. Seung, E. Shamir, and N. Tishby, "Selective sampling using the query by committee algorithm," in Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, 1993.

....of the classifier(s) The selected data will then be labeled by a human or an oracle, and be added to the training set (to retrain the classifier(s) This procedure can be repeated, and our goal is to label as little data as possible to achieve a certain performance. Examples of this approach are [3, 5, 8, 9, 11]. This second approach is usually called active learning in the literature. In order to distinguish from it, we shall thus call the first approach passive partially supervised learning in this paper. Although there have been many previous studies on enhancing classification performance by using ....

....1 x (5) is significant. This indicates that we prefer a data x such that its projection ff x is small (margin is small) and its size is large (x x is large) To prefer a data that has a small margin is quite intuitive based on previous studies of committee based algorithms such as [5, 11]: the label of the most uncertain data is likely to reveal most important information. To prefer large x is less intuitive at the first glance. However, this criterion is also quite natural since in a logistic model, if x is small (the extreme case is x = 0) it is inherent uncertain so that its ....

Y. Freund, H.S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28(2-3):133--168, 1997.

....logarithmic time, they also operate under more restrictive conditions than stochasticcomparison search. The general idea of maximizing the expected information from a query has also been pursued in the machine learning literature under the name Active Learning or Learning with Queries [4]. Active learning techniques have been shown to significantly outperform simple probability ranking for document classification [5] We know of no application of active learning techniques to database retrieval. 2.3 Simultaneous comparisons Bringing the problem even closer to reality, suppose ....

Yoav Freund, H. Sebastian Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the query by committee algorithm. In Advances in Neural Information Processing Systems, Cambridge, MA, 1993. MIT Press.

....question examined in this paper is whether there can be any advantage in studying learning and active classi cation together ; see Section 3. Our task, of learning active classi ers, is also distinct from the task of actively learning (passive) classi ers. For example, Ang87, Ang88] KMT93] [FSST97], consider the learning with membership queries model, in which the learner can request labels of examples as it is learning. Recall however that our learner is seeking optimally inexpensive active classi ers, rather than optimally accurate passive ones; moreover, we focus primarily on a 21 ....

Yoav Freund, H. Sebastian Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133, 1997.

....be iteratively selected for labeling by this approach (Cohn et al. 1996) Frequently, calculating this expected variance reduction in closed form is prohibitively complex and impractical at best. In these cases active learning can proceed by appealing to the Query by Committee (QBC) framework (Freund et al. 1997). Here, instead of selecting a document that maximally reduces classification variance, QBC selects a document for labeling that has high classification variance itself. In a consistent error free learning framework, getting a label for a document with high classification variance eliminates all ....

....itself. In a consistent error free learning framework, getting a label for a document with high classification variance eliminates all hypotheses that do not agree with the label. In these cases QBC provides exponential speed ups in the learning rate over random selection of documents to label (Freund et al. 1997). When the learning task is not so theoretically clean, the intuition behind QBC is that documents with high classification variance lie in regions where the learning algorithm needs help. By getting a true label in that region, significant uncertainty can be eliminated. This approach has been ....

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Freund, Y., Seung, H., Shamir, E., & Tishby, N. (1997). Selective sampling using the query by committee algorithm. Machine Learning, 28(2/3), 133--168.

....to w . If one is willing to assume that there is a hypothesis lying within H that generates the data and that the generating hypothesis is deterministic and that the data are noise free, then strong generalization performance properties of an algorithm that halves version space can also be shown (Freund et al. 1997). For example one can show that the generalization error decreases exponentially with the number of queries. This discussion provides motivation for an approach where we query instances that split the current version space into two equal parts as much as possible. Given an unlabeled instance x ....

....breakeven point performance over the Corn, Trade and Acq Reuters 21578 categories. b) Average test set accuracy over the top ten Reuters 21578 categories. 6. Related Work There have been several studies of active learning for classification. The Query by Committee algorithm (Seung et al. 1992; Freund et al. 1997) uses a prior distribution over hypotheses. This general algorithm has been applied in domains and with classifiers for which specifying and sampling from a prior distribution is natural. They have been used with probabilistic models (Dagan and Engelson, 1995) and specifically with the Naive Bayes ....

Freund, Y., H. Seung, E. Shamir, and N. Tishby: 1997, `Selective Sampling using the Query by Committee Algorithm'. Machine Learning 28, 133--168.

....where the objective is to minimize the expected variance of the predictor. In the above works, the active learner can choose any point in the input space. By contrast, in the query ltering paradigm, the learner can choose to see the label of certain items from a stream of inputs (see e.g. [FSST97]) In the PAC setting, Ang88] showed how the ability to ask questions reduces the problem of identifying certain kinds of boolean functions from NP complete to polynomial time. BHH95] and [TR98] have exended this to active learning of tree structured boolean functions, where the internal nodes ....

Y. Freund, H. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133-168, 1997.

....closed form. Other, more widely used active learning methods attain practicality by optimizing a different, non optimal criterion. For example, uncertainty sampling (Lewis Gale, 1994) selects the example on which the current learner has lowest certainty; Query by Committee (Seung et al. 1992; Freund et al. 1997) selects examples that reduce the size of the version space (Mitchell, 1982) the size of the subset of parameter space that correctly classifies the labeled examples) Tong and Koller s Support Vector Machine method (2000a) is also based on reducing version space size. None of these methods ....

....to the learner from some distribution, and the learner chooses queries from this sample (either as a pool or a stream) From this data oriented perspective, Lewis and Gale (1994) presented the uncertainty sampling algorithm for choosing the example with the greatest uncertainty in predicted label. Freund et al. 1997) showed that uncertainty sampling does not converge to the optimal classifier as quickly as the Query By Committee algorithm (Seung et al. 1992) In the Query By Committee (QBC) approach, the method is to reduce the error of the learner by choosing the instance to be labeled that will ....

[Article contains additional citation context not shown here]

Freund, Y., Seung, H., Shamir, E., & Tishby, N. (1997). Selective sampling using the Query By Committee algorithm. Machine Learning, 28, 133--168.

....of the system. The object, once annotated, gives the maximum information or knowledge gain to the system is selected. In the machine learning literature, the idea of maximizing the expected information from a query has been studied under the name active learning or learning with queries [14]. It was revisited by Cox et al. when they updated the display of the query result in [11] We will present a more detailed survey of the active learning literature in Section II B. In this paper, we will use active learning to improve the performance of a 3D model retrieval system. Note that the ....

Y. Freund, H. S. Seung, E. Shamir, and N. Tishby, "Selective Sampling Using the Query by Committee Algorithm", Advances in Neural Information Processing Systems, Cambridge, MA: MIT Press, 1993.

....paper [64] extends the case study, including more robust EM variants (see subsection 3.3) In [55] the authors try to combine an EM algorithm on a joint probability model (see [65] and subsection 2. 2) with an active learning strategy, namely the queryby committee (QBC) algorithm ( 82] see also [31] and subsection 4.1) to attack an instance of the labeled unlabeled problem in text classi cation. The idea is to overcome stability problems of standard EM by injecting unlabeled points one at a time. Given a large pool of unlabeled data, the authors initialize EM by training on the labeled data ....

....the ability to actively query for labels cannot be of any signi cant advantage if one does not have access to a sample from P (x) Furthermore, in practice, it might be unexpectedly dicult to produce a sample from P (tjx) if P (x) is very small 35 . All these points are discussed in detail in [31], section 1. MacKay [53] discusses Bayesian active learning for multi layer perceptrons. Cohn et al. [19] introduce the general problem, then focus on joint density models of the kind discussed in [35] see also [38] and subsection 2.2) A very general query ltering algorithm is query by ....

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Yoav Freund, H. Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the Query By Committee algorithm. Machine Learning, 28:133-168, 1997.

....decision of the sampled classi ers. ii) The posterior mean the Bayes point machine (BPM) solution [4] can be calculated as an approximation to transduction. iii) The binary entropy of candidate training points can be calculated to determine their information content for active learning [2]. iv) The model evidence [5] can be evaluated for the purpose of model selection. We would like to point out, however, that the KGS is limited in practice to a sample size of m 100 and should thus be thought of as an analytical tool to advance our understanding of the interaction of kernel ....

....of candidate training points a task that can be considered as a dual counterpart to Bayesian Transduction. This is particularly useful when the label y of a training point x is more expensive to obtain than the training point x itself. It was shown in the context of Query by Committee [2] that the binary entropy S (x; z) p log 2 p p log 2 p with p = PWjZ m =z ( hW;xi K 0) is an indicator of the information content of a data point x with regard to the learning task. Samples w j from the Bayesian posterior PWjZ m =z make it possible to estimate S for a ....

Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133168, 1997.

....variance of a neural network learner and Belue et al. 38] suggest a query selection criterion for multi layer perceptron classi ers in a multi class setting. An approach that is originally rooted in statistical physics but has been analyzed within a PAC like framework is Query by Committee [39, 40]. This algorithm makes use of a committee of students to estimate the expected information gain of a query and it can be shown that in this case there exists a relation between the two objective functions maximization of the expected information gain and minimization of the expected generalization ....

....by nding a query that splits the committee in two groups of equal size and thus leads to maximum disagreement among the committee. Note, however, that in general queries that maximize the expected information gain do not guarantee a rapid decrease of the generalization error. Freund et al. [40] suggest a variant of QBC that is restricted to a committee of two members for which they can establish a relation between the expected information gain and the expected generalization error. This algorithm is sketched in Algorithm 2. In contrast to most other query algorithms, this variant of ....

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. Selective sampling using the Query by Committee algorithm. Machine Learning, 28:133-168, 1997.

....learner to classify it, and then seeing how uncertain that classi cation was. The idea is that the more uncertain the example, the harder it is, and therefore, the more useful it would be to have this example annotated. 3. 1 Prior Work in Active Learning Seung, Opper and Sompolinsky (1992) and Freund et al. 1997) proposed a theoretical queryby committee approach. Such an approach uses multiple models (or a committee) to evaluate the data, and candidates for annotation (or queries) are drawn from the pool of examples in which the models disagree. Furthermore, Freund et al. prove that, under some ....

Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. 1997. Selective sampling using the query by committee algorithm. Machine Learning, 28:133-168.

....decision of the sampled classifiers. ii) The posterior mean the Bayes point machine (BPM) solution [4] can be calculated as an approximation to transduction. iii) The binary entropy of candidate training points can be calculated to determine their information content for active learning [2]. iv) The model evidence [5] can be evaluated for the purpose of model selection. We would like to point out, however, that the KGS is limited in practice to a sample size of m 100 and should thus be thought of as an analytical tool to advance our understanding of the interaction of kernel ....

....of candidate training points a task that can be considered as a dual counterpart to Bayesian Transduction. This is particularly useful when the label y of a training point x is more expensive to obtain than the training point x itself. It was shown in the context of Query by Committee [2] that the binary entropy S (x; Z) p log 2 p p Gamma log 2 p Gamma with p Sigma = PWjZ m =Z ( Sigma hW; OE (x)i K 0) is an indicator of the information content of a data point x with regard to the learning task. Samples w j from the Bayesian posterior PWjZ m =Z make it ....

Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168, 1997.

....input space used in the modeling [9, 10] In this paper, active learning will mean learning from unlabeled data, where an oracle can be queried for labels of specific instances, with the goal of minimizing the number of oracle queries required. Active learning has been proposed in various forms [2, 10, 11, 12, 17, 23, 24, 27]. We will discuss in more detail the earlier works in active learning related to the approach used in this paper. One approach to active learning is uncertainty sampling in which instances in the data that need to be labeled are iteratively identified based on some measure that suggests that the ....

Y. Freund, H. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168, 1997.

....be overcome when a large set of unlabeled training data is available. In this case the second type of active learning, sample selection, can often be applied: The learner examines many unlabeled examples, and selects only the most informative ones for learning (Seung, Opper, Sompolinsky, 1992; Freund, Seung, Shamir, Tishby, 1997; Cohn, Atlas, Ladner, 1994; Lewis Catlett, 1994; Lewis Gale, 1994) In this paper, we address the problem of sample selection for training a probabilistic classifier. Classification in this framework is performed by a probability based model which, given an input example, assigns a score ....

....this framework is performed by a probability based model which, given an input example, assigns a score to each possible classification and selects that with the highest score. Our research follows theoretical work on sample selection in the Query By Committee (QBC) paradigm (Seung et al. 1992; Freund et al. 1997). We propose a novel empirical scheme for applying the QBC paradigm to probabilistic classification models (allowing label noise) which were not addressed in the original QBC framework (see Section 2.2) In this committee based selection scheme, the learner receives a stream of unlabeled examples ....

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Freund, Y., Seung, H. S., Shamir, E., & Tishby, N. (1997). Selective sampling using the Query By Committee algorithm. Machine Learning, 28, 133--168.

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Y. Freund, H. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Macine Learning, 28:133--168, 1997.

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Y. Freund, H. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Macine Learning, 28:133--168, 1997.

.... x to is G(xjV) H(Pr h2V [h(x) 1] 1) Pr h2V [h(x) 1] Delta I(x; 1) Pr h2V [h(x) Gamma1] Delta I(x; Gamma1) where H is the binary entropy, i.e. H(p) Gammap log p Gamma (1 Gamma p) log(1 Gamma p) tk = 3fffi ln 3fi is a correction of the expression given at ([6]) Theorem 1 (Freund et al. 6] If a concept class C has VC dimension 0 d 1 and the expected information gain from the queries to Label Oracle made by QBC are uniformly lower bounded by g 0 bits, then the following holds with probability larger than 1 Gamma fi over the choice of the ....

.... = 1] 1) Pr h2V [h(x) 1] Delta I(x; 1) Pr h2V [h(x) Gamma1] Delta I(x; Gamma1) where H is the binary entropy, i.e. H(p) Gammap log p Gamma (1 Gamma p) log(1 Gamma p) tk = 3fffi ln 3fi is a correction of the expression given at ( 6] Theorem 1 (Freund et al. [6]) If a concept class C has VC dimension 0 d 1 and the expected information gain from the queries to Label Oracle made by QBC are uniformly lower bounded by g 0 bits, then the following holds with probability larger than 1 Gamma fi over the choice of the target concept, the sequence of ....

[Article contains additional citation context not shown here]

Y. Freund, H. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Macine Learning, 28:133--168, 1997.

....presented by Seung et al. is Query By Committee (QBC) 8] in which the learning algorithm is presented at each step with a new instance drawn at random. It then measures the uncertainty of the predicted label for the presented instance and decides whether to query for the label. Freund et al. [5] analyzed this algorithm and showed that when certain conditions hold, one can reduce exponentially the number of labels needed, and use only O(log 1= labels compared to O(1= that a Passive learning algorithm will normally use. Later, in [2] this algorithm was shown to be ecient from the ....

....m 2 ; 2: Note that in the deterministic case, the assumption that there is a positive lower bound on p(f i j ) is not necessary. In fact, if has VC dimension d then with probability of at least 1 , I(f (m) d log em d 2 log 1 which is similar to the bound presented in [5]. 2.2 Information Processing Inequality The above result indicates that the information from a set of observations is bounded with high probability. However, even if the information derived from the full set of observations is small, it is still conceivable that there might be a subset of these ....

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Y. Freund, H. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Macine Learning, 28:133-168, 1997.

....task of learning an unknown target concept out of a class of concepts by means of query the target labels at random sample of instances, has generated many studies and experimental works in recent years. In this work we re examine the Query By Committee (QBC) algorithm, formulated and analyzed at [SOS92, FSST97]. QBC is an active learning algorithm [CAL90] which incorporate a relevance test for a potential label. Having access to a stream of unlabeled instances, the relevance test lters out the instances for which it assigns a low value, trying to minimize the number of labels used while learning. The ....

....where H is the binary entropy, i.e. H(p) p log p (1 p) log(1 p) We proceed by quoting the main theoretical result about QBC, give some explanations and brie y outline the main contribution of the present paper, which show how to implement eciently the relevance test. Theorem 1 (Freund et al. [FSST97]) If a concept class C has VC dimension 0 d 1 and the expected information gain of the queries to Label oracle made by QBC are uniformly lower bounded by g 0 bits, then the following holds with probability greater than 1 over the selection of the target concept, the sequence of ....

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Y. Freund, H. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Macine Learning, 28:133-168, 1997.

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Freund, Yoav, H. Sebastion Seung, Eli Shamir, and Naftali Tishby. 1997. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168.

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Y. Freund, S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28(2/3):133--168, 1997.

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Y. Freund, S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning Journal, 28:133--168, 1997.

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Yoav Freund, H. Sebastian Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168, 1997.

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Freund, Y., Seung, H. S., Shamir, E., & Tishby, N. (1997). Selective sampling using the query by committee algorithm. Machine Learning, 28, 133--168.

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. In Machine Learning, pages 133--168, 1997.

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Freund, Y., Seung, H. S., Shamir, E., & Tishby, N. (1997). Selective sampling using the query by committee algorithm. Machine Learning, 28, 133--168.

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Freund, Y., Seung, H. S., Shamir, E., & Tishby, N. (1997). Selective sampling using the query by committee algorithm. Machine Learning, 28, 133--168.

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Freund, Y., Seung, H. S., Shamir, E., & Tishby, N. (1997). Selective sampling using the query by committee algorithm. Machine Learning, 28, 133--168.

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Yoav Freund, H. Sebastian Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133-- 168, 1997.

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby, `Selective sampling using the query by committee algorithm', Machine Learning, 28(2-3), 133--168, (1997).

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28(2-3):133--168, 1997.

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Freund, Y., Seung, H.S., Shamir, E., Tishby, N.: Selective sampling using the query by committee algorithm. Machine Learning 28 (1997) 133--168

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Yoav Freund, H. Sebastian Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168, 1997.

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Yoav Freund, H. Sebastian Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133-- 168, 1997.

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168, 1997.

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Yoav Freund, H. Sebastian Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168, 1997.

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Freund, Y., Seung, H., Shamir, E., Tishby, N., 1997, Selective Sampling Using Query by Committee Algorithm, Machine Learning, 28, 133-168.

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Y. Freund, H. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168, 1997.

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Yoav Freund, H. Sebastian Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the query by committee algorithm. earning, 28(2--3):133--168, AugustSeptember 1997.

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby, "Selective Sampling Using the Query by Committee Algorithm", Advances in Neural Information Processing Systems, Cambridge, MA: MIT Press, 1993.

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby, "Selective Sampling Using the Query by Committee Algorithm", Advances in Neural Information Processing Systems, Cambridge, MA: MIT Press, 1993.

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Y. Freund, S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133--168, 1997.

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133-68, 1997.

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Y. Freund, H. S. Seung, E. Shamir, and N. Tishby. Selective sampling using the query by committee algorithm. Machine Learning, 28:133-168, 1997.

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Yoav Freund, H. Sebastian Seung, Eli Shamir, and Naftali Tishby. 1997. Selective sampling using the query by committee algorithm. Machine Learning, 28(2-3):133--168.

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