MIA: A Framework for Certified Robustness of Time-Series Classification and Forecasting Against Temporally-Localized Perturbations

Recent literature demonstrates that times-series forecasting/classification are sensitive to input perturbations. However, the defenses for time-series models are relatively under-explored. In this paper, we propose \textbf{M}asking \textbf{I}mputing \textbf{A}ggregation (MIA), a plug-and-play framework to provide an arbitrary deterministic time-series model with certified robustness against temporally-localized perturbations (also known as $\ell_0$-norm localized perturbations), which is to our knowledge the first $\ell_0$-norm defense for time-series models. Our main insight is to let an occluding mask move across the input series, guaranteeing that, for an arbitrary localized perturbation there must exist at least a mask that completely remove out the perturbation, so that our prediction on this masked series is uninfluenced. Remarkably, MIA is high-availability as it still works even if we only have query access to the pretrained model. Furthermore, as there is no dedicated defense against $\ell_0$-norm perturbations for time-series models, we specifically adapt two matrix-based defenses to time-series models for comparison. Extensive experiments show that MIA yields stronger robustness as well as practicality.