  In large-scale classification problems, the data set always be faced with
frequent updates when a part of the data is added to or removed from the
original data set. In this case, conventional incremental learning, which
updates an existing classifier by explicitly modeling the data modification, is
more efficient than retraining a new classifier from scratch. However,
sometimes, we are more interested in determining whether we should update the
classifier or performing some sensitivity analysis tasks. To deal with these
such tasks, we propose an algorithm to make rational inferences about the
updated linear classifier without exactly updating the classifier.
Specifically, the proposed algorithm can be used to estimate the upper and
lower bounds of the updated classifier's coefficient matrix with a low
computational complexity related to the size of the updated dataset. Both
theoretical analysis and experiment results show that the proposed approach is
superior to existing methods in terms of tightness of coefficients' bounds and
computational complexity.
