Interpretable Anomaly Detection via Discrete Optimization

Anomaly detection is essential in many application domains, such as cyber security, law enforcement, medicine, and fraud protection. However, the decision-making of current deep learning approaches is notoriously hard to understand, which often limits their practical applicability. To overcome this limitation, we propose a framework for learning inherently interpretable anomaly detectors from sequential data. More specifically, we consider the task of learning a deterministic finite automaton (DFA) from a given multi-set of unlabeled sequences. We show that this problem is computationally hard and develop two learning algorithms based on constraint optimization. Moreover, we introduce novel regularization schemes for our optimization problems that improve the overall interpretability of our DFAs. Using a prototype implementation, we demonstrate that our approach shows promising results in terms of accuracy and F1 score.

Specification sketching for Linear Temporal Logic

Virtually all verification and synthesis techniques assume that the formal specifications are readily available, functionally correct, and fully match the engineer's understanding of the given system. However, this assumption is often unrealistic in practice: formalizing system requirements is notoriously difficult, error-prone, and requires substantial training. To alleviate this severe hurdle, we propose a fundamentally novel approach to writing formal specifications, named specification sketching for Linear Temporal Logic (LTL). The key idea is that an engineer can provide a partial LTL formula, called an LTL sketch, where parts that are hard to formalize can be left out. Given a set of examples describing system behaviors that the specification should or should not allow, the task of a so-called sketching algorithm is then to complete a given sketch such that the resulting LTL formula is consistent with the examples. We show that deciding whether a sketch can be completed falls into the complexity class NP and present two SAT-based sketching algorithms. We also demonstrate that sketching is a practical approach to writing formal specifications using a prototype implementation.