Boosting Certificate Robustness for Time Series Classification with Efficient Self-Ensemble

Recently, the issue of adversarial robustness in the time series domain has garnered significant attention. However, the available defense mechanisms remain limited, with adversarial training being the predominant approach, though it does not provide theoretical guarantees. Randomized Smoothing has emerged as a standout method due to its ability to certify a provable lower bound on robustness radius under $\ell_p$-ball attacks. Recognizing its success, research in the time series domain has started focusing on these aspects. However, existing research predominantly focuses on time series forecasting, or under the non-$\ell_p$ robustness in statistic feature augmentation for time series classification~(TSC). Our review found that Randomized Smoothing performs modestly in TSC, struggling to provide effective assurances on datasets with poor robustness. Therefore, we propose a self-ensemble method to enhance the lower bound of the probability confidence of predicted labels by reducing the variance of classification margins, thereby certifying a larger radius. This approach also addresses the computational overhead issue of Deep Ensemble~(DE) while remaining competitive and, in some cases, outperforming it in terms of robustness. Both theoretical analysis and experimental results validate the effectiveness of our method, demonstrating superior performance in robustness testing compared to baseline approaches.