COLEP：通过概率电路实现可认证鲁棒的推理-学习共形预测
COLEP: Certifiably Robust Learning-Reasoning Conformal Prediction via Probabilistic Circuits
AI总结：
针对对抗性扰动破坏共形预测覆盖率的问题，提出COLEP框架，结合概率电路实现可认证鲁棒的推理-学习共形预测，理论上提供端到端覆盖率认证，实验显示在多个数据集上显著提升认证覆盖率。
摘要：
共形预测在假设数据可交换的情况下，为任意黑盒机器学习模型构建统计上严格的预测集方面展现出了显著的性能。然而，推理过程中的即使是微小的对抗性扰动也可能违反可交换性假设，挑战覆盖率保证，并导致经验覆盖率的后续下降。在这项工作中，我们提出了一种通过概率电路实现的可认证鲁棒的推理-学习共形预测框架（COLEP），该框架包含一个数据驱动的学习组件，用于训练统计模型以学习不同的语义概念，以及一个推理组件，用于编码知识并表征所训练模型之间的关系以进行逻辑推理。为了实现精确且高效的推理，我们在推理组件中采用了概率电路（PCs）。理论上，我们在存在有界对抗性扰动的情况下，为COLEP提供了端到端的预测覆盖率认证。我们还考虑了校准集有限大小的情况，提供了认证覆盖率。此外，我们证明了只要知识模型的效用非平凡，COLEP相比单一模型能够实现更高的预测覆盖率和准确性。在实证方面，我们展示了认证覆盖率的有效性和紧致性，证明了COLEP在包括GTSRB、CIFAR10和AwA2在内的多个数据集上的鲁棒共形预测。我们展示了COLEP在GTSRB上实现了高达12%的认证覆盖率提升，在CIFAR-10上实现了9%的提升，在AwA2上实现了14%的提升。
英文摘要：
Conformal prediction has shown spurring performance in constructing statistically rigorous prediction sets for arbitrary black-box machine learning models, assuming the data is exchangeable. However, even small adversarial perturbations during the inference can violate the exchangeability assumption, challenge the coverage guarantees, and result in a subsequent decline in empirical coverage. In this work, we propose a certifiably robust learning-reasoning conformal prediction framework (COLEP) via probabilistic circuits, which comprise a data-driven learning component that trains statistical models to learn different semantic concepts, and a reasoning component that encodes knowledge and characterizes the relationships among the trained models for logic reasoning. To achieve exact and efficient reasoning, we employ probabilistic circuits (PCs) within the reasoning component. Theoretically, we provide end-to-end certification of prediction coverage for COLEP in the presence of bounded adversarial perturbations. We also provide certified coverage considering the finite size of the calibration set. Furthermore, we prove that COLEP achieves higher prediction coverage and accuracy over a single model as long as the utilities of knowledge models are non-trivial. Empirically, we show the validity and tightness of our certified coverage, demonstrating the robust conformal prediction of COLEP on various datasets, including GTSRB, CIFAR10, and AwA2. We show that COLEP achieves up to 12% improvement in certified coverage on GTSRB, 9% on CIFAR-10, and 14% on AwA2.
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