Semi-Parametric Uncertainty Bounds for Binary Classification
This provides a theoretical foundation for uncertainty quantification in binary classification, which is important for risk assessment in applications like medical diagnosis or finance, though it appears incremental as it builds on existing kernel and resampling techniques.
The paper tackles the problem of estimating uncertainty bounds for binary classification by constructing non-asymptotic confidence regions for the regression function, which is key to the Bayes optimal classifier. The authors propose three kernel-based semi-parametric resampling methods and prove they guarantee exact coverage probabilities and strong consistency.
The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal classifier, moreover, besides providing optimal predictions, it can also assess the risk of misclassification. We aim at building non-asymptotic confidence regions for the regression function and suggest three kernel-based semi-parametric resampling methods. We prove that all of them guarantee regions with exact coverage probabilities and they are strongly consistent.