# Adversarial Framework with Certified Robustness for Time-Series Domain via Statistical Features

arXiv: https://arxiv.org/abs/2207.04307 · HTML: https://mlsanity.com/paper/2207.04307/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 71 references that are in the map.
- First posted on arXiv 9 Jul 2022.

## Builds on (most cited first, 30 of 33)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (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)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [Black-box Generation of Adversarial Text Sequences to Evade Deep Learning Classifiers](https://mlsanity.com/paper/1801.04354/) (2018)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Spatially Transformed Adversarial Examples](https://mlsanity.com/paper/1801.02612/) (2018)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Technical Report on the CleverHans v2.1.0 Adversarial Examples Library](https://mlsanity.com/paper/1610.00768/) (2016)
- [A Study and Comparison of Human and Deep Learning Recognition Performance Under Visual Distortions](https://mlsanity.com/paper/1705.02498/) (2017)
- [RayS: A Ray Searching Method for Hard-label Adversarial Attack](https://mlsanity.com/paper/2006.12792/) (2020)
- [Deep Learning for Financial Applications : A Survey](https://mlsanity.com/paper/2002.05786/) (2020)
- [Functional Adversarial Attacks](https://mlsanity.com/paper/1906.00001/) (2019)
- [Towards Crafting Text Adversarial Samples](https://mlsanity.com/paper/1707.02812/) (2017)
- [Adversarial Attacks on Deep Neural Networks for Time Series Classification](https://mlsanity.com/paper/1903.07054/) (2019)
- [Highly comparative feature-based time-series classification](https://mlsanity.com/paper/1401.3531/) (2014)
- [Adversarial Attacks on Time Series](https://mlsanity.com/paper/1902.10755/) (2019)
- [Distributed and parallel time series feature extraction for industrial big data applications](https://mlsanity.com/paper/1610.07717/) (2016)
- [A Frank-Wolfe Framework for Efficient and Effective Adversarial Attacks](https://mlsanity.com/paper/1811.10828/) (2018)
- [Adversarial Examples in Deep Learning for Multivariate Time Series Regression](https://mlsanity.com/paper/2009.11911/) (2020)

## Built on by (most cited first, 7 of 7)

- [Probabilistically Tightened Linear Relaxation-based Perturbation Analysis for Neural Network Verification](https://mlsanity.com/paper/2507.05405/) (2025)
- [Boosting Certified Robustness for Time Series Classification with Efficient Self-Ensemble](https://mlsanity.com/paper/2409.02802/) (2024)
- [Forecasting Fails: Unveiling Evasion Attacks in Weather Prediction Models](https://mlsanity.com/paper/2512.08832/) (2025)
- [Fortifying Time Series: DTW-Certified Robust Anomaly Detection](https://mlsanity.com/paper/2605.07690/) (2026)
- [Certified Adversarial Robustness via Partition-based Randomized Smoothing](https://mlsanity.com/paper/2409.13546/) (2024)
- [Exposing Vulnerabilities in Explanation for Time Series Classifiers via Dual-Target Attacks](https://mlsanity.com/paper/2602.02763/) (2026)
- [Adversarial Robustness of Time-Series Classification for Crystal Collimator Alignment](https://mlsanity.com/paper/2604.06289/) (2026)

## Abstract (arXiv)

Time-series data arises in many real-world applications (e.g., mobile health) and deep neural networks (DNNs) have shown great success in solving them. Despite their success, little is known about their robustness to adversarial attacks. In this paper, we propose a novel adversarial framework referred to as Time-Series Attacks via STATistical Features (TSA-STAT)}. To address the unique challenges of time-series domain, TSA-STAT employs constraints on statistical features of the time-series data to construct adversarial examples. Optimized polynomial transformations are used to create attacks that are more effective (in terms of successfully fooling DNNs) than those based on additive perturbations. We also provide certified bounds on the norm of the statistical features for constructing adversarial examples. Our experiments on diverse real-world benchmark datasets show the effectiveness of TSA-STAT in fooling DNNs for time-series domain and in improving their robustness. The source code of TSA-STAT algorithms is available at https://github.com/tahabelkhouja/Time-Series-Attacks-via-STATistical-Features