Robust Multivariate Time-Series Forecasting: Adversarial Attacks and Defense Mechanisms

This work studies the threats of adversarial attack on multivariate probabilistic forecasting models and viable defense mechanisms. Our studies discover a new attack pattern that negatively impact the forecasting of a target time series via making strategic, sparse (imperceptible) modifications to the past observations of a small number of other time series. To mitigate the impact of such attack, we have developed two defense strategies. First, we extend a previously developed randomized smoothing technique in classification to multivariate forecasting scenarios. Second, we develop an adversarial training algorithm that learns to create adversarial examples and at the same time optimizes the forecasting model to improve its robustness against such adversarial simulation. Extensive experiments on real-world datasets confirm that our attack schemes are powerful and our defense algorithms are more effective compared with baseline defense mechanisms. Understanding the robustness for time-series models has been a long-standing issue with applications across many disciplines such as climate change (Mudelsee, 2019), financial market analysis (Andersen et al., 2005; Hallac et al., 2017), down-stream decision systems in retail (Böse et al., 2017), resource planning for cloud computing (Park et al., 2019; 2020), and optimal control of vehicles (Kim et al., 2020). In particular, the notion of robustness defines how sensitive the model output is when authentic data is (potentially) perturbed with noises. In practice, as observation data are often corrupted by measurement noises, it is important to develop statistical forecasting models that are less sensitive to such noises (Brown, 1957; Brockwell & Davis, 2009; Taylor & Letham, 2018) or more stable against outliers that might arise from such corruption (Connor et al., 1994; Gelper et al., 2010; Liu & Zhang, 2021; Wang & Tsay, 2021).