Channel Matters: Estimating Channel Influence for Multivariate Time Series

TL;DR

This work addresses the gap in channel-aware interpretability for multivariate time series by introducing Channel-wise Influence (ChInf), a first method to quantify cross-channel influence in MTS through a channel-wise influence matrix $\boldsymbol{M}_{CInf}$. By deriving a channel-specific analogue of TracIn, the authors create two downstream, ChInf-based algorithms for MTS anomaly detection and channel pruning, and demonstrate superior performance relative to both traditional influence functions and model-centric baselines on real-world datasets. The approach offers a scalable, data-centric perspective with practical benefits in anomaly detection accuracy and dataset efficiency via channel pruning, while also enabling interpretable insights into inter-channel relationships. Overall, ChInf provides a principled tool to analyze and leverage channel information in MTS, with significant implications for efficiency and interpretability across domains.

Abstract

The influence function serves as an efficient post-hoc interpretability tool that quantifies the impact of training data modifications on model parameters, enabling enhanced model performance, improved generalization, and interpretability insights without the need for expensive retraining processes. Recently, Multivariate Time Series (MTS) analysis has become an important yet challenging task, attracting significant attention. While channel extremely matters to MTS tasks, channel-centric methods are still largely under-explored for MTS. Particularly, no previous work studied the effects of channel information of MTS in order to explore counterfactual effects between these channels and model performance. To fill this gap, we propose a novel Channel-wise Influence (ChInf) method that is the first to estimate the influence of different channels in MTS. Based on ChInf,we naturally derived two channel-wise algorithms by incorporating ChInf into classic MTS tasks. Extensive experiments demonstrate the effectiveness of ChInf and ChInf-based methods in critical MTS analysis tasks, such as MTS anomaly detection and MTS data pruning. Specifically, our ChInf-based methods rank top-1 among all methods for comparison, while previous influence functions do not perform well on MTS anomaly detection tasks and MTS data pruning problem. This fully supports the superiority and necessity of ChInf.

Figures (5)

• Figure 1: (a)-(b): The ablation study of ChInf for iTransformer and GCN-LSTM on SMAP and SMD dataset. Our ChInf can enhance MTS performance, while the conventional influence fails. (c): The relationship between the number of parameters used to calculate influence and the anomaly detection performance on different datasets.
• Figure 2: Visual illustration of different channels on ETTh1 dataset.
• Figure 3: (a)-(c): The comparison experiment between sample pruning and channel pruning on three datasets. From left to right are the Electricity dataset, the Solar Energy dataset, and the Traffic dataset. The evaluation metric used is mean squared error (MSE), with lower values indicating better performance. The horizontal axis represents the remaining ratio of the dataset.
• Figure 4: Visual illustration of the anomaly score of different methods on SMAP dataset.
• Figure : ChInf based anomaly detection

Theorems & Definitions (3)

• Theorem 3.1
• Remark 3.2
• proof