arXiv:2604.01502stat.MLcs.LG2026-04被引 2

提出非单调损失下可靠风险控制方法,解决实际中预测集大小与精度矛盾问题。

Conformal Risk Control under Non-Monotone Losses: Theory and Finite-Sample Guarantees

论文配图:Conformal Risk Control under Non-Monotone Losses: Theory and Finite-Sample Guarantees
图 1 · 摘自论文原文
  • 在有限网格上选择参数时,通过校准样本量与网格分辨率关系确保风险控制有效
  • 证明了风险超出目标水平的误差按√(log m / n)收敛,且该速率最优
  • 适用于真实数据中的多标签分类和目标检测,对不确定性更敏感的场景更优

共形风险控制(CRC)可在无需分布假设下实现对期望损失的可控。现有理论通常假设损失随调参参数单调递减,但实际中因覆盖率与效率的权衡,损失常呈非单调性。本文研究在有限网格上选择调参时的非单调损失下的CRC,发现其有效性取决于校准样本量n与网格大小m的关系。当n相对于m足够大时,可实现可靠风险控制。针对有界损失,建立了有限样本保证:超出目标水平α的超额风险以√(log m / n)为阶,且该率是极小极大最优的。在额外结构假设(如Lipschitz连续、单调性)下得到更精细结果,并通过重要性加权拓展至分布偏移场景。合成多标签分类与真实目标检测实验表明,显式考虑有限样本不确定性的方法比依赖单调变换的方法更具稳定性,同时保持较小的预测集尺寸。

原文摘要 · Abstract (English)

Conformal risk control (CRC) provides distribution-free guarantees for controlling the expected loss at a user-specified level. Existing theory typically assumes that the loss decreases monotonically with a tuning parameter that governs the size of the prediction set. However, this assumption is often violated in practice, where losses may behave non-monotonically due to competing objectives such as coverage and efficiency. In this paper, we study CRC under non-monotone loss functions when the tuning parameter is selected from a finite grid, a setting commonly arising in thresholding and discretized decision rules. Revisiting a known counterexample, we show that the validity of CRC without monotonicity depends critically on the relationship between the calibration sample size and the grid resolution. In particular, reliable risk control can still be achieved when the calibration sample is sufficiently large relative to the grid size. We establish a finite-sample guarantee for bounded losses over a grid of size $m$, showing that the excess risk above the target level $α$ scales on the order of $\sqrt{\log(m)/n}$, where $n$ is the calibration sample size. A matching lower bound demonstrates that this rate is minimax optimal. We also derive refined guarantees under additional structural conditions, including Lipschitz continuity and monotonicity, and extend the analysis to settings with distribution shift via importance weighting. Numerical experiments on synthetic multilabel classification and real object detection data illustrate the practical implications of non-monotonicity. Methods that explicitly account for finite-sample uncertainty achieve more stable risk control than approaches based on monotonicity transformations, while maintaining competitive prediction set sizes.

风险控制共形推断非单调性有限样本

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