Active learning with logistic models featuring simultaneous variable and subject selection

Abstract

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.