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Modern computing and communication technologies can make data collection procedures very efficient, while our ability to analyze and extract information from large data sets is hard-pressed to keep up with our capacity for data collection. If we are interested in learning a classification/prediction rule that was not considered in the original data collection procedure, then there is usually a lack of label information in the original data. Thus, how to start with minimum number of labeled data and aggressively selected most informative samples for being labeled becomes an important issue. The thoughts of active learning, with subjects to be selected sequentially without using label information, is a possible outlet for this situation. In addition, if we can identify variables, from the lengthy variable list of the data set, for constructing an effective classification rule with good interpretation ability will be better. Here, we propose an active learning procedure targeted the maximum area under the receiver operating characteristic curve via a commonly use logistic model, which can sequentially select the effective informative subjects and variables, simultaneously. We discuss the asymptotic properties of the proposed procedure and illustrate it with some synthesized and real data sets. [ABSTRACT FROM AUTHOR]

Sequential change-point analysis, which identifies a change of probability distribution in an infinite sequence of random observations, has important applications in many fields. A good method should detect a change point as soon as possible, and keep a low amount of false alarms. As one of the most popular methods, Shiryaev-Roberts (SR) procedure holds many optimalities. However, its implementation requires the pre-change and post-change distributions to be known, which is not achievable in practice. In this paper, we construct a nonparametric version of the SR procedure by embedding different versions of empirical likelihood, assuming two training samples, before and after change, are available for parameter estimations. Simulations are conducted to compare the performance of the proposed method with existing methods. The results show that when the underlying distribution is unknown, and training sample sizes are small, the proposed modified procedure shows advantage by giving a smaller delay of detection. [ABSTRACT FROM AUTHOR]