Intensive algorithmic efforts have been made to enable the rapid improvements of certificated robustness for complex ML models recently. However, current robustness certification methods are only able to certify under a limited perturbation radius. Given that existingpure data-driven statistical approaches have reached a bottleneck, in this paper, we propose to integrate statistical ML modelswithknowledge (expressed aslogical rules) asareasoningcomponent using Markovlogic networks (MLN), so as to further improvethe overall certified robustness.

As machine learning (ML) being applied to many mission-critical scenarios, certifying ML model robustness becomes increasingly important. Many previous works focuses on the robustness of independent ML and ensemble models, and can only certify a very small magnitude of the adversarial perturbation. In this paper, we take a different viewpoint and improve learning robustness by going beyond independent ML and ensemble models. We aim at promoting the generic Sensing-Reasoning machine learning pipeline which contains both the sensing (e.g. deep neural networks) and reasoning (e.g. Markov logic networks (MLN)) components enriched with domain knowledge. Can domain knowledge help improve learning robustness? Can we formally certify the end-to-end robustness of such an ML pipeline? We first theoretically analyze the computational complexity of checking the provable robustness in the reasoning component. We then derive the provable robustness bound for several concrete reasoning components. We show that for reasoning components such as MLN and a specific family of Bayesian networks it is possible to certify the robustness of the whole pipeline even with a large magnitude of perturbation which cannot be certified by existing work. Finally, we conduct extensive real-world experiments on large scale datasets to evaluate the certified robustness for Sensing-Reasoning ML pipelines.