Nested conformal prediction and quantile out-of-bag ensemble methods
This work provides a more flexible and efficient approach to conformal prediction, which is significant for researchers and practitioners in machine learning seeking reliable uncertainty quantification, though it is incremental as it builds on existing methods.
The paper tackles the problem of generating valid prediction sets in conformal prediction by introducing a nested framework that unifies existing nonconformity scores and extends them to aggregation schemes like cross-conformal and out-of-bag methods, resulting in a new algorithm (QOOB) that performs best or close to best on all simulated and real datasets.
Conformal prediction is a popular tool for providing valid prediction sets for classification and regression problems, without relying on any distributional assumptions on the data. While the traditional description of conformal prediction starts with a nonconformity score, we provide an alternate (but equivalent) view that starts with a sequence of nested sets and calibrates them to find a valid prediction set. The nested framework subsumes all nonconformity scores, including recent proposals based on quantile regression and density estimation. While these ideas were originally derived based on sample splitting, our framework seamlessly extends them to other aggregation schemes like cross-conformal, jackknife+ and out-of-bag methods. We use the framework to derive a new algorithm (QOOB, pronounced cube) that combines four ideas: quantile regression, cross-conformalization, ensemble methods and out-of-bag predictions. We develop a computationally efficient implementation of cross-conformal, that is also used by QOOB. In a detailed numerical investigation, QOOB performs either the best or close to the best on all simulated and real datasets. Code for QOOB is available at https://github.com/aigen/QOOB.