Super-Level-Set Regression: Conditional Quantiles via Volume Minimization
Constructing minimum-volume prediction regions that satisfy conditional coverage is a fundamental challenge in multivariate regression. Standard approaches rely on explicitly estimating the full conditional density and subsequently thresholding it. This two-step plug-in process is notoriously difficult, sensitive to estimation errors, and computationally expensive. One would like to instead optimize the region directly. Formulating a direct solution is challenging, however, because it requires minimizing a volume objective that is coupled with the conditional quantiles of the model's own estimation error. In this work, we address this challenge. We introduce super-level-set regression (SL...
| Authors | Sacha Braun, Michael I. Jordan, Francis Bach |
|---|---|
| Primary category | stat.ML |
| Published | 7 May 2026 |
| Last updated at source | 7 May 2026 |
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