提出可凸优化的集合预测损失函数，平衡置信集大小与覆盖率
A Convex Loss Function for Set Prediction with Optimal Trade-offs Between Size and Conditional Coverage
- 基于洛瓦兹扩展构造凸损失，实现覆盖与集合大小的最优权衡
- 在合成数据上优于仅关注边缘覆盖率的方法，提升条件覆盖率
- 适合需要精确不确定性估计的分类与回归任务
我们研究了以集合预测提供显式不确定性估计的监督学习问题。通过使用恰克特积分（即洛瓦兹扩展），我们提出了一个针对实值函数水平集生成的非递减子集函数的凸损失函数。该损失函数能够在条件概率覆盖率与集合大小之间实现最优权衡，集合大小由非递减次模函数度量。我们还提出了若干仿照具有非对称损失的二分类损失函数和准则的扩展，并展示了如何自然地获得具有优化条件覆盖率的集合。我们推导出高效的优化算法，基于随机梯度下降或重加权最小二乘法，通过一系列在分类与回归任务上的合成数据实验验证了方法的有效性，结果表明其优于仅追求边缘覆盖率的方法。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。