# Boosting Certified Robustness for Time Series Classification with Efficient Self-Ensemble

arXiv: https://arxiv.org/abs/2409.02802 · HTML: https://mlsanity.com/paper/2409.02802/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 23 of 23)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [MACER: Attack-free and Scalable Robust Training via Maximizing Certified Radius](https://mlsanity.com/paper/2001.02378/) (2020)
- [Adversarial Attacks on Deep Neural Networks for Time Series Classification](https://mlsanity.com/paper/1903.07054/) (2019)
- [Boosting Randomized Smoothing with Variance Reduced Classifiers](https://mlsanity.com/paper/2106.06946/) (2021)
- [Reliable Conflictive Multi-View Learning](https://mlsanity.com/paper/2402.16897/) (2024)
- [Adversarial Attacks on Time Series](https://mlsanity.com/paper/1902.10755/) (2019)
- [Benchmarking adversarial attacks and defenses for time-series data](https://mlsanity.com/paper/2008.13261/) (2020)
- [Robust Multivariate Time-Series Forecasting: Adversarial Attacks and Defense Mechanisms](https://mlsanity.com/paper/2207.09572/) (2022)
- [Adversarial Framework with Certified Robustness for Time-Series Domain via Statistical Features](https://mlsanity.com/paper/2207.04307/) (2022)
- [SWAP: Exploiting Second-Ranked Logits for Adversarial Attacks on Time Series](https://mlsanity.com/paper/2309.02752/) (2023)
- [Towards an Awareness of Time Series Anomaly Detection Models' Adversarial Vulnerability](https://mlsanity.com/paper/2208.11264/) (2022)
- [Dynamic Defense Approach for Adversarial Robustness in Deep Neural Networks via Stochastic Ensemble Smoothed Model](https://mlsanity.com/paper/2105.02803/) (2021)
- [Rethinking Randomized Smoothing from the Perspective of Scalability](https://mlsanity.com/paper/2312.12608/) (2023)

## Built on by (most cited first, 1 of 1)

- [NERVE Attacks: Breaking AI-Powered Brain-Computer Interfaces](https://mlsanity.com/paper/2609.08971/) (2026)

## Abstract (arXiv)

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 ℓp-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-ℓp 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.