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We introduce a novel sensitivity analysis framework for large scaleclassification problems that can be used when a small number of instances areincrementally added or removed. For quickly updating the classifier in such asituation, incremental learning algorithms have been intensively studied in theliterature. Although they are much more efficient than solving the optimizationproblem from scratch, their computational complexity yet depends on the entiretraining set size. It means that, if the original training set is large,completely solving an incremental learning problem might be still ratherexpensive. To circumvent this computational issue, we propose a novel frameworkthat allows us to make an inference about the updated classifier withoutactually re-optimizing it. Specifically, the proposed framework can quicklyprovide a lower and an upper bounds of a quantity on the unknown updatedclassifier. The main advantage of the proposed framework is that thecomputational cost of computing these bounds depends only on the number ofupdated instances. This property is quite advantageous in a typical sensitivityanalysis task where only a small number of instances are updated. In this paperwe demonstrate that the proposed framework is applicable to various practicalsensitivity analysis tasks, and the bounds provided by the framework are oftensufficiently tight for making desired inferences.

Quick sensitivity analysis for incremental data modification and its application to leave-one-out CV in linear classification problems