Least Ambiguous Set-Valued Classifiers with Bounded Error Levels
This work addresses the need for more informative and reliable classification in multiclass tasks, particularly for ambiguous observations, though it is incremental as it builds on existing single-label classifiers.
The paper tackles the problem of ambiguous instances in classification by introducing set-valued classifiers that guarantee user-defined coverage levels while minimizing expected set size, deriving oracle classifiers from conditional probability level sets and developing estimators with good asymptotic and finite sample properties.
In most classification tasks there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classifiers output sets of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framework for multiclass set-valued classification, where the classifiers guarantee user-defined levels of coverage or confidence (the probability that the true label is contained in the set) while minimizing the ambiguity (the expected size of the output). We first derive oracle classifiers assuming the true distribution to be known. We show that the oracle classifiers are obtained from level sets of the functions that define the conditional probability of each class. Then we develop estimators with good asymptotic and finite sample properties. The proposed estimators build on existing single-label classifiers. The optimal classifier can sometimes output the empty set, but we provide two solutions to fix this issue that are suitable for various practical needs.