A Convex Loss Function for Set Prediction with Optimal Trade-offs Between Size and Conditional Coverage
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912782239137792 |
|---|---|
| author | Bach, Francis |
| author_facet | Bach, Francis |
| contents | We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{á}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions obtained as level sets of a real-valued function. This loss function allows optimal trade-offs between conditional probabilistic coverage and the ''size'' of the set, measured by a non-decreasing submodular function. We also propose several extensions that mimic loss functions and criteria for binary classification with asymmetric losses, and show how to naturally obtain sets with optimized conditional coverage. We derive efficient optimization algorithms, either based on stochastic gradient descent or reweighted least-squares formulations, and illustrate our findings with a series of experiments on synthetic datasets for classification and regression tasks, showing improvements over approaches that aim for marginal coverage. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Convex Loss Function for Set Prediction with Optimal Trade-offs Between Size and Conditional Coverage Bach, Francis Machine Learning Optimization and Control We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{á}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions obtained as level sets of a real-valued function. This loss function allows optimal trade-offs between conditional probabilistic coverage and the ''size'' of the set, measured by a non-decreasing submodular function. We also propose several extensions that mimic loss functions and criteria for binary classification with asymmetric losses, and show how to naturally obtain sets with optimized conditional coverage. We derive efficient optimization algorithms, either based on stochastic gradient descent or reweighted least-squares formulations, and illustrate our findings with a series of experiments on synthetic datasets for classification and regression tasks, showing improvements over approaches that aim for marginal coverage. |
| title | A Convex Loss Function for Set Prediction with Optimal Trade-offs Between Size and Conditional Coverage |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2512.19142 |