COLEP: Certifiably Robust Learning-Reasoning Conformal Prediction via Probabilistic Circuits

TL;DR

COLEP introduces a certifiably robust conformal prediction framework using probabilistic circuits, enhancing prediction coverage and accuracy under adversarial perturbations for black-box models.

Contribution

The paper presents a novel learning-reasoning conformal prediction method with end-to-end certification against adversarial attacks, integrating probabilistic circuits for efficient reasoning.

Findings

Up to 12% improvement in certified coverage on GTSRB

Achieves higher coverage and accuracy than single models

Validated on datasets GTSRB, CIFAR10, and AwA2

Abstract

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.