Agnostic Active Learning Without Constraints

We present and analyze an agnostic active learning algorithm that works without keeping a version space. This is unlike all previous approaches where a restricted set of candidate hypotheses is maintained throughout learning, and only hypotheses from this set are ever returned. By avoiding this version space approach, our algorithm sheds the computational burden and brittleness associated with maintaining version spaces, yet still allows for substantial improvements over supervised learning for classification

Active classification with comparison queries

We study an extension of active learning in which the learning algorithm may ask the annotator to compare the distances of two examples from the boundary of their label-class. For example, in a recommendation system application (say for restaurants), the annotator may be asked whether she liked or disliked a specific restaurant (a label query); or which one of two restaurants did she like more (a comparison query). We focus on the class of half spaces, and show that under natural assumptions, such as large margin or bounded bit-description of the input examples, it is possible to reveal all the labels of a sample of size $n$ using approximately $O(\log n)$ queries. This implies an exponential improvement over classical active learning, where only label queries are allowed. We complement these results by showing that if any of these assumptions is removed then, in the worst case, $\Omega(n)$ queries are required. Our results follow from a new general framework of active learning with additional queries. We identify a combinatorial dimension, called the \emph{inference dimension}, that captures the query complexity when each additional query is determined by $O(1)$ examples (such as comparison queries, each of which is determined by the two compared examples). Our results for half spaces follow by bounding the inference dimension in the cases discussed above.Comment: 23 pages (not including references), 1 figure. The new version contains a minor fix in the proof of Lemma 4.

Online Importance Weight Aware Updates

An importance weight quantifies the relative importance of one example over another, coming up in applications of boosting, asymmetric classification costs, reductions, and active learning. The standard approach for dealing with importance weights in gradient descent is via multiplication of the gradient. We first demonstrate the problems of this approach when importance weights are large, and argue in favor of more sophisticated ways for dealing with them. We then develop an approach which enjoys an invariance property: that updating twice with importance weight $h$ is equivalent to updating once with importance weight $2h$. For many important losses this has a closed form update which satisfies standard regret guarantees when all examples have $h=1$. We also briefly discuss two other reasonable approaches for handling large importance weights. Empirically, these approaches yield substantially superior prediction with similar computational performance while reducing the sensitivity of the algorithm to the exact setting of the learning rate. We apply these to online active learning yielding an extraordinarily fast active learning algorithm that works even in the presence of adversarial noise