We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise. We demonstrate the effectiveness of our approach by designing algorithms with improved noise tolerance guarantees for learning linear separators. We consider the malicious noise model of Valiant and the adversarial label noise model of Kearns, Schapire, and Sellie. For malicious noise, where the adversary can corrupt an @math of fraction both the label part and the feature part, we provide a polynomial-time algorithm for learning linear separators in @math under the uniform distribution with near information-theoretic optimal noise tolerance of @math . We also get similar improvements for the adversarial label noise model. We obtain similar results for more general classes of distributions including isotropic log-concave distributions. In addition, our algorithms achieve a label complexity whose dependence on the error parameter @math is exponentially better than that of any passive algorithm. This provides the first polynomial-time active learning algorithm for learning linear separators in the presence of adversarial label noise, as well as the first analysis of active learning under the malicious noise model.
@cite_20 @cite_48 online learning algorithms in the selective sampling framework are presented, where labels must be actively queried before they are revealed. Under the assumption that the label conditional distribution is a linear function determined by a fixed target vector, they provide bounds on the regret of the algorithm and on the number of labels it queries when faced with an adaptive adversarial strategy of generating the instances. As pointed out in @cite_48 , these results can also be converted to a distributional PAC setting where instances @math are drawn i.i.d. In this setting they obtain exponential improvement in label complexity over passive learning. These interesting results and techniques are not directly comparable to ours. Our framework is not restricted to halfspaces. Another important difference is that (as pointed out in @cite_7 ) the exponential improvement they give is not possible in the noiseless version of their setting. In other words, the addition of linear noise defined by the target makes the problem easier for active sampling. By contrast RCN can only make the classification task harder than in the realizable case.
@cite_48 @cite_7 @cite_20
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We present a new online learning algorithm in the selective sampling framework, where labels must be actively queried before they are revealed. We prove bounds on the regret of our algorithm and on the number of labels it queries when faced with an adaptive adversarial strategy of generating the instances. Our bounds both generalize and strictly improve over previous bounds in similar settings. Additionally, our selective sampling algorithm can be converted into an efficient statistical active learning algorithm. We extend our algorithm and analysis to the multiple-teacher setting, where the algorithm can choose which subset of teachers to query for each label. Finally, we demonstrate the effectiveness of our techniques on a real-world Internet search problem. Active learning is a protocol for supervised machine learning, in which a learning algorithm sequentially requests the labels of selected data points from a large pool of unlabeled data. This contrasts with passive learning, where the labeled data are taken at random. The objective in active learning is to produce a highly-accurate classifier, ideally using fewer labels than the number of random labeled data sufficient for passive learning to achieve the same. This article describes recent advances in our understanding of the theoretical benefits of active learning, and implications for the design of effective active learning algorithms. Much of the article focuses on a particular technique, namely disagreement-based active learning, which by now has amassed a mature and coherent literature. It also briefly surveys several alternative approaches from the literature. The emphasis is on theorems regarding the performance of a few general algorithms, including rigorous proofs where appropriate. However, the presentation is intended to be pedagogical, focusing on results that illustrate fundamental ideas, rather than obtaining the strongest or most general known theorems. The intended audience includes researchers and advanced graduate students in machine learning and statistics, interested in gaining a deeper understanding of the recent and ongoing developments in the theory of active learning. We introduce efficient margin-based algorithms for selective sampling and filtering in binary classification tasks. Experiments on real-world textual data reveal that our algorithms perform significantly better than popular and similarly efficient competitors. Using the so-called Mammen-Tsybakov low noise condition to parametrize the instance distribution, and assuming linear label noise, we show bounds on the convergence rate to the Bayes risk of a weaker adaptive variant of our selective sampler. Our analysis reveals that, excluding logarithmic factors, the average risk of this adaptive sampler converges to the Bayes risk at rate N ?(1+?)(2+?) 2(3+?) where N denotes the number of queried labels, and ?>0 is the exponent in the low noise condition. For all @math this convergence rate is asymptotically faster than the rate N ?(1+?) (2+?) achieved by the fully supervised version of the base selective sampler, which queries all labels. Moreover, for ??? (hard margin condition) the gap between the semi- and fully-supervised rates becomes exponential.