Selective Prediction from Agreement: A Lipschitz-Consistent Version Space Approach
This work addresses the problem of reliable selective classification with abstention for fixed unlabeled pools, offering a principled method with theoretical guarantees.
The paper introduces a selective prediction method using agreement among Lipschitz-consistent classifiers in a transductive setting, achieving certified predictions when all consistent heads agree. The approach guarantees label consistency and provides a greedy querying strategy with approximation guarantees.
We consider selective classification with abstention in the fixed-pool (or transductive) setting, where the unlabeled pool is given beforehand and only a subset of points can be queried for labels. Our main insight is to view selective prediction through agreement: given queried labels and Lipschitz margin constraints in an embedding space, the version space of Lipschitz-consistent classification heads is well defined. We obtain upper and lower Lipschitz margin bounds that define, for each pool point, a set of certified valid labels containing the prediction of every head in the version space. The model therefore predicts only when the label is forced (i.e., all consistent heads agree), and abstains otherwise. We also propose a monotone submodular geometric proxy for budgeted querying, and show that a greedy algorithm retains the standard approximation factor.