Title: Channel Matters: Estimating Channel Influence for Multivariate Time Series
Venue: NeurIPS 2025
Accepted: yes
Keywords: multivariate time series; channel-wise influence function; Data-centric AI
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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes using influence functions, which estimate the counterfactual effect between training data and model performance, as a data-centric perspective to better understand and analyze multivariate time series (MTS). Addressing the limitation of existing influence functions, such as TimeInf, which overlook the impact of different channels in MTS, the authors introduce a new influence function called ChInf. This method is applied to two key MTS tasks: anomaly detection and data pruning. The results demonstrate that ChInf consistently performs well across various methods, validating its effectiveness.\n\nSTRENGTHS AND WEAKNESSES:\nPros:\n1. Applying influence functions to analyze MTS is a novel and meaningful idea.\n2. The paper is well-structured and easy to follow, progressing logically from the introduction of influence functions, through their refinement, to the empirical validation of ChInf across multiple tasks.\n3. The experiments are thorough, demonstrating ChInf’s effectiveness from multiple perspectives and on various tasks.\n\nCons:\n1. The citation formatting is inconsistent and needs revision.\n2. There are concerns about the definition of the influence score in the two downstream tasks:\n* For example, in anomaly detection, why is the score defined as the maximum across all channels rather than the average? This choice requires further empirical justification, especially since uniformly distributed influence across channels might be overlooked.\n* In Equation (4), why is the score computed only for a channel's influence on itself? Shouldn't channel i potentially influence all channels, not just itself?\n\nQUESTIONS:\n1. See Weakness #2 above.\n2. In Section 5.1.3, you claim that the original TracIn is ineffective because it doesn't differentiate between channels. This conclusion seems somewhat unconvincing: shouldn't a global influence function still yield meaningful results? According to your reasoning, would TracIn and ChInf perform similarly on univariate time series? Further explanation or empirical validation of this point would be helpful.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a method for quantifying how removing a channel from a multivariate time-series affects the loss on a another channel. This metric is applied to standard time-series tasks including anomaly detection and data pruning.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper is generally well written and the method seems sound albeit somewhat incremental. In the context of anomaly detection, it seems to amount to a different aggregation of per-channel influence (max instead of sum) if I understand correctly. Still the method seems useful in practice. The empirical analysis is well done and includes simple baselines that seem to outperform many competing deep models. Some discussion of this results would be helpful, along with why the proposed method is stronger. This leads me to a larger point:\n\nA common view regarding anomaly detection is that some prior knowledge is needed regarding the down-stream task in order to define what constitutes an anomaly [1,2]. This makes evaluation and comparison of anomaly detection methods challenging. I think this work could be stronger if there was at least a discussion on the *kinds* of anomalies the method targets. For instance it would seem to me that the method should be strong at detecting anomalies when individual channels are \"broken\", meaning they do not follow their usual pattern in relation to other channels (for instance, this work [3] tackles such anomalies in games by modeling correlations between channels). This might be in contrast to methods that are better at detecting when the entire time-series behaves abnormaly.\n\nI would also recommend that the authors revise some of the method explanation, for instance after eq. 1, to improve clarity.\n\n[1] Winkens, Jim, et al. \"Contrastive training for improved out-of-distribution detection.\" arXiv preprint arXiv:2007.05566 (2020).\n[2] Le Lan, Charline, and Laurent Dinh. \"Perfect density models cannot guarantee anomaly detection.\" Entropy 23.12 (2021): 1690.\n[3] Lymperopoulos, Panagiotis, Yukun Li, and Liping Liu. \"Exploiting variable correlation with masked modeling for anomaly detection in time series.\" NeurIPS 2022 Workshop on Robustness in Sequence Modeling. 2022.\n\nQUESTIONS:\nRe-iterating my previous questions:\n- Why do simple baseline methods outperform most deep methods, and what differentiates ChInf? Even if that is mentioned in a cited work, a sentence explanation would be helpful to aid in interpretation of the results.\n- What kind of anomalies do you expect ChInf to be strong at detecting and where do you expect it to perform less favorably. Is there something about the tested datasets that indicates that they are well suited for ChInf? Are there cases where you expect the proposed method to underperform? Some additional discussion of this point would be helpful.\n\nLIMITATIONS:\nSee my question regarding anomalies that may be \"missed\" by this method.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work proposes Channel-wise Influence (ChInf), a novel method that extends influence functions to multivariate time series (MTS) data by estimating the influence of individual channels. While influence functions have traditionally been used to analyze the effect of training data on model parameters without retraining, their application to channel-centric analysis in MTS tasks has been largely unexplored. To address this gap, the authors introduce ChInf and derive two ChInf-based algorithms for common MTS tasks. Experimental results show that these methods significantly outperform existing approaches in MTS anomaly detection and data pruning, highlighting the necessity and effectiveness of channel-wise influence analysis.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. This study is interesting, which investigate the influence functions to multivariate time series (MTS) data by estimating the influence of individual channels.\n\n2. The writing and organization of this paper are good.\n\n3. The proposed method shows excellent performance.\n\nHowever, I have some concerns as follows.\n\nWeaknesses:\n\n1. Could you provide additional experiments on MTS anomaly detection using the UEA archives, as prior works on MTS anomaly detection typically include evaluations on these datasets?\n\n2. Can you provide more theoretical analyses on this work? For instance, the computational complexity?\n\n3. It's clear that the influence of MTS in deep learning has not been well studied, and how to estimate the influence of different channels in MTS is critical. However, what are the challenges in the process remains unclear. More discussions are required.\n\n4. The authors are suggested to add more discussions into the related work. For instance, the discussions on the MTS anomaly detection and forecasting are limited. Additional discussions on the categories of MTS anomaly detection or forecasting can enhance the readability of this work.\n\nQUESTIONS:\n1. Could you provide additional experiments on MTS anomaly detection using the UEA archives, as prior works on MTS anomaly detection typically include evaluations on these datasets?\n\n2. Can you provide more theoretical analyses on this work? For instance, the computational complexity?\n\n3. It's clear that the influence of MTS in deep learning has not been well studied, and how to estimate the influence of different channels in MTS is critical. However, what are the challenges in the process remains unclear. More discussions are required.\n\n4. The authors are suggested to add more discussions into the related work. For instance, the discussions on the MTS anomaly detection and forecasting are limited. Additional discussions on the categories of MTS anomaly detection or forecasting can enhance the readability of this work.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes Channel-wise Influence (ChInf), a novel influence function for Multivariate Time Series (MTS) data, which estimates the influence of each channel, allowing both interpretability and efficient channel pruning. The authors validate their method through experiments on anomaly detection and channel pruning, demonstrating its effectiveness, interpretability, and generality across multiple datasets and model architectures (e.g., iTransformer, PatchTST).\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. This paper introduces the Channel-wise Influence Function, a new method designed to assess and interpret the influence relationships among different channels in MTS data. In contrast, the traditional methods assess the impact of entire data samples on model performance. \n2. ChInf proves to be a versatile approach, achieving good performance in two MTS tasks—anomaly detection and channel pruning.\n\nWeakness:\n1. The method requires computing gradients individually for each channel, leading to a computational complexity that scales linearly with the number of channels, which may pose challenges when applied to large-scale multivariate time series data.\n2. The method is evaluated on two representative tasks, without investigating its applicability to other important MTS problems, which may limit the demonstration of its broader generalizability.\n\nQUESTIONS:\n1. For online anomaly detection, is it feasible to update ChInf incrementally?\n2. In the context of real-world datasets such as Electricity, is there any case study, qualitative analysis or interpretability experiment demonstrating whether the channels ranked by ChInf correspond to domain-critical variables or sensors? Do these rankings align with known domain knowledge from the respective domains?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-07"}