  Modern computing and communication technologies can make data collection
procedures very efficient. However, our ability to analyze large data sets
and/or to extract information out from them is hard-pressed to keep up with our
capacities for data collection. Among these huge data sets, some of them are
not collected for any particular research purpose. For a classification
problem, this means that the essential label information may not be readily
obtainable, in the data set in hands, and an extra labeling procedure is
required such that we can have enough label information to be used for
constructing a classification model. When the size of a data set is huge, to
label each subject in it will cost a lot in both capital and time. Thus, it is
an important issue to decide which subjects should be labeled first in order to
efficiently reduce the training cost/time. Active learning method is a
promising outlet for this situation, because with the active learning ideas, we
can select the unlabeled subjects sequentially without knowing their label
information. In addition, there will be no confirmed information about the
essential variables for constructing an efficient classification rule. Thus,
how to merge a variable selection scheme with an active learning procedure is
of interest. In this paper, we propose a procedure for building binary
classification models when the complete label information is not available in
the beginning of the training stage. We study an model-based active learning
procedure with sequential variable selection schemes, and discuss the results
of the proposed procedure from both theoretical and numerical aspects.
