Every day, huge volumes of sensory, transactional, and web data are continuously generated as streams, which need to be analyzed online as they arrive. Streaming data can be considered as one of the main sources of what is called big data. While predictive modeling for data streams and big data have received a lot of attention over the last decade, many research approaches are typically designed for well-behaved controlled problem settings, overlooking important challenges imposed by real-world applications. This article presents a discussion on eight open challenges for data stream mining. Our goal is to identify gaps between current research and meaningful applications, highlight open problems, and define new application-relevant research directions for data stream mining. The identified challenges cover the full cycle of knowledge discovery and involve such problems as: protecting data privacy, dealing with legacy systems, handling incomplete and delayed information, analysis of complex data, and evaluation of stream mining algorithms. The resulting analysis is illustrated by practical applications and provides general suggestions concerning lines of future research in data stream mining.

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In contrast to ever increasing volumes of automatically generated data, human annotation capacities remain limited. Thus, fast active learning approaches that allow the efficient allocation of annotation efforts gain in importance. Furthermore, cost-sensitive applications such as fraud detection pose the additional challenge of differing misclassification costs between classes. Unfortunately, the few existing cost-sensitive active learning approaches rely on time-consuming steps, such as performing self-labelling or tedious evaluations over samples. We propose a fast, non-myopic, and cost-sensitive probabilistic active learning approach for binary classification. Our approach computes the expected reduction in misclassification loss in a labelling candidate's neighbourhood. We derive and use a closedform solution for this expectation, which considers the possible values of the true posterior of the positive class at the candidate's position, its possible label realisations, and the given labelling budget. The resulting myopic algorithm runs in the same linear asymptotic time as uncertainty sampling, while its non-myopic counterpart requires an additional factor of O(m · log m) in the budget size. The experimental evaluation on several synthetic and realworld data sets shows competitive or better classification performance and runtime, compared to several uncertainty sampling-and error-reduction-based active learning strategies, both in cost-sensitive and cost-insensitive settings.