  Feature missing is a serious problem in many applications, which may lead to
low quality of training data and further significantly degrade the learning
performance. While feature acquisition usually involves special devices or
complex process, it is expensive to acquire all feature values for the whole
dataset. On the other hand, features may be correlated with each other, and
some values may be recovered from the others. It is thus important to decide
which features are most informative for recovering the other features as well
as improving the learning performance. In this paper, we try to train an
effective classification model with least acquisition cost by jointly
performing active feature querying and supervised matrix completion. When
completing the feature matrix, a novel target function is proposed to
simultaneously minimize the reconstruction error on observed entries and the
supervised loss on training data. When querying the feature value, the most
uncertain entry is actively selected based on the variance of previous
iterations. In addition, a bi-objective optimization method is presented for
cost-aware active selection when features bear different acquisition costs. The
effectiveness of the proposed approach is well validated by both theoretical
analysis and experimental study.
