用单个二值证书实现更小、更快的鲁棒预测集
Robust Conformal Prediction with a Single Binary Certificate
- 通过可调阈值将样本二值化，仅需一个二值证书即可保证鲁棒性
- 在CIFAR10上仅用150次采样即达理想覆盖率，远低于传统方法的10⁴次
- 无需限制评分函数有界，适合实际部署中复杂模型的鲁棒预测
校准预测（CP）可将任意模型输出转化为具有高概率覆盖真实标签的预测集。鲁棒校准预测（Robust CP）将该保证扩展至最坏情况（对抗性）输入。现有方法通过限制随机平滑的符合度得分来实现鲁棒性，但实践中需大量蒙特卡洛（MC）采样（如每个点约10⁴次）以维持可接受的集合大小。本文提出一种新型鲁棒校准预测方法，即使使用显著减少的MC采样（如在CIFAR10上仅需150次），仍能生成更小的预测集。该方法通过可调（或自动调整）阈值对样本进行二值化，确保覆盖性。关键突破在于：我们证明只需计算一个二值证书即可实现鲁棒性，而无需为每个校准或测试点分别认证。因此本方法更高效且生成更小的鲁棒预测集。此外，我们消除了此前要求评分函数有界的限制。
原文摘要 · Abstract (English)
Conformal prediction (CP) converts any model's output to prediction sets with a guarantee to cover the true label with (adjustable) high probability. Robust CP extends this guarantee to worst-case (adversarial) inputs. Existing baselines achieve robustness by bounding randomly smoothed conformity scores. In practice, they need expensive Monte-Carlo (MC) sampling (e.g. $\sim10^4$ samples per point) to maintain an acceptable set size. We propose a robust conformal prediction that produces smaller sets even with significantly lower MC samples (e.g. 150 for CIFAR10). Our approach binarizes samples with an adjustable (or automatically adjusted) threshold selected to preserve the coverage guarantee. Remarkably, we prove that robustness can be achieved by computing only one binary certificate, unlike previous methods that certify each calibration (or test) point. Thus, our method is faster and returns smaller robust sets. We also eliminate a previous limitation that requires a bounded score function.
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