  Abstaining classifiers have been widely used in cost-sensitive applications
to avoid ambiguous classification and reduce the cost of misclassification.
Previous abstaining classification models rely on cost information, such as a
cost matrix or cost ratio. However, it is difficult to obtain or estimate costs
in practical applications. Furthermore, these abstention models are typically
restricted to a single optimization metric, which may not be the expected
indicator when evaluating classification performance. To overcome such
problems, a multi-objective bounded-abstention (MOBA) model is proposed to
optimize essential metrics. Specifically, the MOBA model minimizes the error
rate of each class under class-dependent abstention constraints. The MOBA model
is then solved using the non-dominated sorting genetic algorithm II, which is a
popular evolutionary multi-objective optimization algorithm. A set of
Pareto-optimal solutions will be generated and the best one can be selected
according to provided conditions (whether costs are known) or performance
demands (e.g., obtaining a high accuracy, F-measure, and etc). Hence, the MOBA
model is robust towards variations in the conditions and requirements. Compared
to state-of-the-art abstention models, MOBA achieves lower expected costs when
cost information is considered, and better performance-abstention trade-offs
when it is not.
