Instance-dependent cost-sensitive parametric learning

Instance-dependent cost-sensitive learning addresses classification problems where each observation has a different misclassification cost. In this paper, we propose cost-sensitive parametric models to minimize the expectation of losses. A loss function incorporating the misclassification costs is defined, which serves as the objective function for obtaining cost-sensitive parameter estimators. The consistency and asymptotic normality of these estimators are established under general conditions, theoretically demonstrating their good performance. Additionally, we derive bounds for the bias introduced when regularizing the optimization problem, which is generally necessary in practice. To conclude, the effectiveness of the proposed estimators is evaluated through an extensive novel simulation study and the analysis of five real data sets, further demonstrating their proficiency in practical settings.