Predictive Value Generalization Bounds
This work addresses the need for more nuanced performance assessment in binary classification, particularly for applications where predictive values are critical, such as medical diagnostics, but it is incremental as it builds on existing generalization theory.
The authors tackled the problem of deriving generalization bounds for positive and negative predictive values in binary classification, which are not directly addressed by standard error rate bounds, and they developed new distribution-free large deviation and uniform convergence bounds for scoring functions.
In this paper, we study a bi-criterion framework for assessing scoring functions in the context of binary classification. The positive and negative predictive values (ppv and npv, respectively) are conditional probabilities of the true label matching a classifier's predicted label. The usual classification error rate is a linear combination of these probabilities, and therefore, concentration inequalities for the error rate do not yield confidence intervals for the two separate predictive values. We study generalization properties of scoring functions with respect to predictive values by deriving new distribution-free large deviation and uniform convergence bounds. The latter bound is stated in terms of a measure of function class complexity that we call the order coefficient; we relate this combinatorial quantity to the VC-subgraph dimension.