Channel-wise Influence: Estimating Data Influence for Multivariate Time Series

2024-08-27

arXiv.org

AI Summary

Quantifying channel importance and performing channel-centric analysis remain challenging in multivariate time series (MTS) modeling. Method: This paper introduces the Channel-level Influence Function (CIF), the first influence-function-based approach tailored for MTS, grounded in robust statistics theory. CIF leverages first-order gradient approximations and dataset-averaged gradients to estimate the causal contribution of each input channel to model outputs. Unlike conventional global influence functions, CIF enables fine-grained, interpretable channel importance assessment and supports principled channel pruning. Results: Extensive evaluation across multiple real-world MTS datasets demonstrates that CIF significantly improves anomaly detection and forecasting accuracy over baseline methods. Moreover, CIF is the only existing framework capable of enabling stable, performance-preserving channel pruning while maintaining model robustness—establishing it as a novel, theoretically grounded quantification paradigm for MTS channel analysis.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Computer Vision: Interpretability, Explainability, and Transparency

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

The influence function, a technique from robust statistics, measures the impact on model parameters or related functions when training data is removed or modified. This effective and valuable post-hoc method allows for studying the interpretability of machine learning models without requiring costly model 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 training 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 that leverages the more informative average gradient of the data set. Additionally, we demonstrate how this influence function can be used to estimate the impact 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 dataset, the original influence function performs worse than our method and even fail for the channel pruning problem, which demonstrate the superiority and necessity of channel-wise influence function in MTS analysis tasks.

Problem

• Estimating channel influence in multivariate time series analysis
• Developing first method for counterfactual channel effects exploration
• Improving anomaly detection and data pruning through channel influence

Innovation

• Proposes Channel-wise Influence method for MTS
• Estimates channel impacts without retraining models
• Derives channel-wise algorithms for MTS tasks