DRIFTS: Distributed Robustness for Time Series is Feasible, Distributed, and Fun

As complex machine learning models are increasingly integrated into critical systems, ensuring their robustness, transparency, and trustworthiness becomes essential. Explainability methods that offer formal and verifiable guarantees about model behavior are crucial not only for interpretability but also for robust decision assurance. In this work, we address the problem of generating formally grounded and robustness-aware explanations for classifiers operating in the time series domain. Our main objective is to introduce the concept of a continuous anti reason. We formalize this concept as an Interval Constraint Function (ICF) which, given a classifier and a sample, assigns an interval for each feature value of the sample. An ICF that constitutes a continuous anti reason for a given sample ensures that all data points whose feature values lie within the corresponding intervals are classified differently from the sample class. Each continuous anti reason is associated with a cost, quantifying the extent of perturbation required to induce a class change. The higher the cost of a continuous anti reason, less robust the classifier is on that sample. Therefore such a property is paramount for precisely characterizing the robustness boundaries of the classifier on a sample-wise basis. Given that computing a continuous anti reason is coNP-complete, we develop the framework called Distributed Robustness Interval for Time Series (DRIFTS), a distributed algorithm that leverages an in-memory key-value store to coordinate multiple workers. The effectiveness and scalability of our approach are validated empirically on Random Forest models using univariate time series datasets from the UCR Archive.