Channel-wise Influence: Estimating Data Influence for Multivariate Time Series
Keywords: channel-wise influence function, mutivariate time series
Abstract: The influence function, a robust statistics technique, is an effective post-hoc method that measures the impact of modifying or removing training data on model parameters, offering valuable insights into model interpretability without requiring costly retraining. It would provide extensions like increasing model performance, improving model generalization, and offering interpretability. Recently, Multivariate Time
Series (MTS) analysis has become an important yet challenging task, attracting significant attention. However, there is no preceding research on the influence functions of MTS to shed light on the effects of modifying the channel of MTS. Given that each channel in an MTS plays a crucial role in its analysis, it is essential to characterize the influence of different channels. To fill this gap, we propose a channel-wise influence function, which is the first method that can estimate the influence of different channels in MTS, utilizing a first-order gradient approximation. Additionally, we demonstrate how this influence function can be used to estimate the influence of a channel in MTS. Finally, we validated the accuracy and effectiveness of our influence estimation function in critical MTS analysis tasks, such as MTS anomaly detection and MTS forecasting. According to abundant experiments on real-world datasets, the original influence function performs worse than our method and even fails for the channel pruning problem, which demonstrates the superiority and necessity of the channel-wise influence function in MTS analysis.
Primary Area: learning on time series and dynamical systems
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Submission Number: 2768
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