We state and analyze the first active learning algorithm which works in the presence of arbitrary forms of noise. The algorithm, A2 (for Agnostic Active), relies only upon the assumption that the samples are drawn i.i.d. from a fixed distribution. We show that A2 achieves an exponential improvement (i.e., requires only O � ln 1 ɛ samples to find an ɛ-optimal classifier) over the usual sample complexity of supervised learning, for several settings considered before in the realizable case. These include learning threshold classifiers and learning homogeneous linear separators with respect to an input distribution which is uniform over the unit sphere. 1.

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The key idea behind active learning is that a machine learning algorithm can achieve greater accuracy with fewer labeled training instances if it is allowed to choose the data from which is learns. An active learner may ask queries in the form of unlabeled instances to be labeled by an oracle (e.g., a human annotator). Active learning is well-motivated in many modern machine learning problems, where unlabeled data may be abundant but labels are difficult, time-consuming, or expensive to obtain. This report provides a general introduction to active learning and a survey of the literature. This includes a discussion of the scenarios in which queries can be formulated, and an overview of the query strategy frameworks proposed in the literature to date. An analysis of the empirical and theoretical evidence for active learning, a summary of several problem setting variants, and a discussion

We present a simple, agnostic active learning algorithm that works for any hypothesis class of bounded VC dimension, and any data distribution. Our algorithm extends a scheme of Cohn, Atlas, and Ladner to the agnostic setting, by (1) reformulating it using a reduction to supervised learning and (2) showing how to apply generalization bounds even for the non-i.i.d. samples that result from selective sampling. We provide a general characterization of the label complexity of our algorithm. This quantity is never more than the usual PAC sample complexity of supervised learning, and is exponentially smaller for some hypothesis classes and distributions. We also demonstrate improvements experimentally.

Abstract. This paper aims to shed light on achievable limits in active learning. Using minimax analysis techniques, we study the achievable rates of classification error convergence for broad classes of distributions characterized by decision boundary regularity and noise conditions. The results clearly indicate the conditions under which one can expect significant gains through active learning. Furthermore we show that the learning rates derived are tight for “boundary fragment ” classes in ddimensional feature spaces when the feature marginal density is bounded from above and below. 1

Abstract. We present a framework for margin based active learning of linear separators. We instantiate it for a few important cases, some of which have been previously considered in the literature. We analyze the effectiveness of our framework both in the realizable case and in a specific noisy setting related to the Tsybakov small noise condition. 1

A selective sampling algorithm is a learning algorithm for classification that, based on the past observed data, decides whether to ask the label of each new instance to be classified. In this paper, we introduce a general technique for turning linear-threshold classification algorithms from the general additive family into randomized selective sampling algorithms. For the most popular algorithms in this family we derive mistake bounds that hold for individual sequences of examples. These bounds

We describe and explore a new perspective on the sample complexity of active learning. In many situations where it was generally believed that active learning does not help, we find that active learning does help in the limit, often with exponential improvements in sample complexity. This contrasts with the traditional analysis of active learning problems such as non-homogeneous linear separators or depth-limited decision trees, in which Ω(1/ɛ) lower bounds are common; we point out that such results must be interpreted carefully, and that finding an ɛ-good classifier can always be accomplished with a number of samples asymptotically smaller than any such bound. These new insights arise from a subtle variation on the traditional definition of sample complexity, not previously recognized in the active learning literature. 1

We present a practical and statistically consistent scheme for actively learning binary classifiers under general loss functions. Our algorithm uses importance weighting to correct sampling bias, and by controlling the variance, we are able to give rigorous label complexity bounds for the learning process. 1.

Active learning methods seek to reduce the number of labeled examples needed to train an effective classifier, and have natural appeal in spam filtering applications where trustworthy labels for messages may be costly to acquire. Past investigations of active learning in spam filtering have focused on the pool-based scenario, where there is assumed to be a large, unlabeled data set and the goal is to iteratively identify the best subset of examples for which to request labels. However, even with optimizations this is a costly approach. We investigate an online active learning scenario where the filter is exposed to a stream of messages which must be classified one at a time. The filter may only request a label for a given message immediately after it has been classified. The goal is to achieve strong online classification performance with few label requests. This is a novel scenario for low-cost active spam filtering, fitting for application in large-scale systems. We draw from the label efficient machine learning literature to investigate several approaches to selective sampling in this scenario using linear classifiers. We show that online active learning can dramatically reduce labeling and training costs with negligible additional overhead while maintaining high levels of classification performance.