  Classification is an important task in many fields including biomedical
research and machine learning. Traditionally, a classification rule is
constructed based a bunch of labeled data. Recently, due to technological
innovation and automatic data collection schemes, we easily encounter with data
sets containing large amounts of unlabeled samples. Because to label each of
them is usually costly and inefficient, how to utilize these unlabeled data in
a classifier construction process becomes an important problem. In machine
learning literature, active learning or semi-supervised learning are popular
concepts discussed under this situation, where classification algorithms
recruit new unlabeled subjects sequentially based on the information learned
from previous stages of its learning process, and these new subjects are then
labeled and included as new training samples. From a statistical aspect, these
methods can be recognized as a hybrid of the sequential design and stochastic
approximation procedure. In this paper, we study sequential learning procedures
for building efficient and effective classifiers, where only the selected
subjects are labeled and included in its learning stage. The proposed algorithm
combines the ideas of Bayesian sequential optimal design and uncertainty
sampling. Computational issues of the algorithm are discussed. Numerical
results using both synthesized data and real examples are reported.
