A Convex Optimization Framework for Active Learning

In many image/video/web classification problems, we have access to a large number of unlabeled samples. However, it is typically expensive and time consuming to obtain labels for the samples. Active learning is the problem of progressively selecting and annotating the most informative unlabeled samples, in order to obtain a high classification performance. Most existing active learning algorithms select only one sample at a time prior to retraining the classifier. Hence, they are computationally expensive and cannot take advantage of parallel labeling systems such as Mechanical Turk. On the other hand, algorithms that allow the selection of multiple samples prior to retraining the classifier, may select samples that have significant information overlap or they involve solving a non-convex optimization. More importantly, the majority of active learning algorithms are developed for a certain classifier type such as SVM. In this paper, we develop an efficient active learning framework based on convex programming, which can select multiple samples at a time for annotation. Unlike the state of the art, our algorithm can be used in conjunction with any type of classifiers, including those of the family of the recently proposed Sparse Representation-based Classification (SRC). We use the two principles of classifier uncertainty and sample diversity in order to guide the optimization program towards selecting the most informative unlabeled samples, which have the least information overlap. Our method can incorporate the data distribution in the selection process by using the appropriate dissimilarity between pairs of samples. We show the effectiveness of our framework in person detection, scene categorization and face recognition on real-world datasets.