TimeInf: Time Series Data Contribution via Influence Functions
Time Series Data Contribution;Time Series Anomaly Detection
Yes
No ethics review needed.
See above.
The idea of inferring interpretability and anomaly analysis by measuring the contribution of time series data to the model's output is quite novel. The mathematical derivation is well-developed, and the details are thorough.
This paper presents an interesting approach to time series interpretability research—by using noise perturbations to measure the contribution of data to the model. However, the method designed by the authors is a theoretical extension of existing approaches and lacks more extensive experimental evidence to demonstrate its effectiveness.
1. Compared to existing methods, the advantages of this approach are not fully emphasized, and the innovative aspects are not clearly defined. The main contribution of the paper can be seen as an extension of existing theory, but the method primarily involves deriving formulas based on Equation (3) and considering the Mixture of \( \delta z^{[m]} \). This operation has limited significance for theoretical extension and does not effectively demonstrate the contribution claimed. I do not believe it addresses the shortcomings of existing methods.
2. The paper conducts experiments on anomaly detection, interpretability, and mislabeled error in datasets. However, the paper does not discuss current state-of-the-art baselines in anomaly detection, such as methods based on LLMs or DCdetector. Moreover, the AUC and F1 results differ significantly from the original work. While the authors' skepticism about dataset quality is commendable, more evidence is needed to support this claim, as only partial visualizations of the data are presented. Additionally, the ablation experiments in the appendix are limited to parameter experiments. Based on my experience, complex theoretical methods often perform unsatisfactorily in neural network training, and more evidence is required to validate the effectiveness of the theory.
3. Compared to traditional machine learning papers, there is no clear and complete process to present the designed algorithm, such as the input, output, and objective function. The majority of the paper is focused on theoretical formulas and related comparisons, making it difficult to understand
Yes
No ethics review needed.
Please reply to the above weaknesses if I have any misunderstandings. Thank you.

Another question: Can the proposed model process multivariate time series?
1. The paper is well-written and easy to follow.
2. The presented solution is technically solid.
3. The experiments on anomaly detection can demonstrate the efficacy of the proposed method.
This paper presents a new method for measuring the contribution of different timestamp to the final predictions. The major idea is to leverage influence scores to assign model predictions to individual time points while preserving temporal structures between the time points. Experiments in anomaly detection can verify the effectiveness of the proposed method.
1. The relationship between the proposed model and unsupervised anomaly detection is unclear and should be further explained.

2. The model's generalization ability to other time series tasks (e.g., forecasting, imputation) is uncertain. Specifically, how would the contribution score of historical timestamps be measured for future time points?

3. There is no discussion on scalability. How does the method perform as the number of historical time points increases?
Yes
No ethics review needed.
See weakness.
The primary technical strength of TimeInf lies in its novel and theoretically sound approach to data contribution estimation in time series. It successfully extends influence functions to handle temporal dependencies, addressing a significant gap in time series analysis that previous methods overlooked. The method is built on a strong mathematical foundation combining robust statistics with innovative use of overlapping blocks to preserve temporal structure. This theoretical rigor is balanced with practical efficiency, as TimeInf proves to be computationally faster than deep learning alternatives while remaining scalable to large datasets with millions of time points. The method provides clear, quantifiable influence scores and intuitive visualizations that help users understand both anomaly patterns and forecasting behaviors. Its comprehensive evaluation across multiple real-world datasets demonstrates consistent improvement over existing approaches in both effectiveness and efficiency.
This paper introduces TimeInf, a novel method for estimating data contribution in time series datasets using influence functions. Unlike previous data contribution methods that primarily focus on i.i.d. settings, TimeInf specifically addresses the challenges of temporal dependencies in time series data. The method works by analyzing overlapping blocks of consecutive time points to preserve temporal structure, then uses influence functions to measure how individual time points impact model predictions. TimeInf's key innovation is its ability to integrate data values across consecutive time series observations while accounting for different temporal arrangements of data points. The authors demonstrate TimeInf's effectiveness through extensive experiments on real-world datasets, showing it outperforms existing methods in both identifying harmful anomalies and helpful time points for forecasting. The method is particularly noteworthy for its computational efficiency, interpretable results through visualizations, and strong performance in practical applications, while being theoretically grounded in robust statistics and autoregressive models.
1. Methodological Limitations:
The paper’s core claim about their “distinctive integration” considering various temporal patterns seems to overlap significantly with existing attention mechanisms, without adequately differentiating itself. The theoretical justification for TimeInf lacks rigorous analysis of its properties, such as consistency or asymptotic behavior. Additionally, the paper doesn’t thoroughly explore the sensitivity of TimeInf to various hyperparameters, like block length or model architecture choices.
	2.	Experimental Issues:
The experimental setup, particularly for anomaly detection tasks, is not clearly described, making result reproduction challenging. The reported results differ significantly from those in original papers for baseline methods, raising questions about comparison fairness. Important baselines in time series anomaly detection such as MTAD-GAT[1], TransAD[2] are missing, limiting the ability to fully assess TimeInf’s performance relative to state-of-the-art methods.  [1] and [2] are using the unspervised learning to learn the distribution and don't use the "clean data assumption" as well. The paper also lacks a comprehensive evaluation of TimeInf’s interpretability claims compared to other approaches.
	3.	Limited Scope and Analysis:
While the paper focuses primarily on anomaly detection tasks, it’s not clear how well TimeInf generalizes to other time series tasks or domains. The computational complexity of TimeInf compared to existing approaches is not thoroughly analyzed, despite mentioning efficiency improvements through conjugate gradient and Hessian-free approaches. The paper lacks a thorough discussion of TimeInf’s limitations or potential failure cases, which is crucial for understanding when and where the method is most applicable. Lastly, the evaluation metrics used are standard (AUC and F1 score), but don’t consider other potentially relevant metrics for time series anomaly detection, such as detection delay or false positive rate at a fixed detection threshold.


[1] Zhao, Hang, et al. "Multivariate time-series anomaly detection via graph attention network." 2020 IEEE international conference on data mining (ICDM). IEEE, 2020.
[2] Tuli, Shreshth, Giuliano Casale, and Nicholas R. Jennings. "TranAD: deep transformer networks for anomaly detection in multivariate time series data." Proceedings of the VLDB Endowment 15.6 (2022): 1201-1214.
Yes
No ethics review needed.
No ethics review needed.
+ Experimentally, TimeInf can effectively identify anomalies in time series. However, in the Data Pruning experiment, the authors claim that TimeInf can identify the most influential time patterns, which appears different from detecting anomalies (removing anomalies should not necessarily lead to a significant drop in model performance). Why is TimeInf able to identify influential time patterns at times, while it detects anomalies at other times? This seems somewhat contradictory.

[1]. Tuli S, Casale G, Jennings N R. TranAD: deep transformer networks for anomaly detection in multivariate time series data[J]. Proceedings of the VLDB Endowment, 2022, 15(6): 1201-1214.

[2]. Xiao C, Gou Z, Tai W, et al. Imputation-based time-series anomaly detection with conditional weight-incremental diffusion models[C]//Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2023: 2742-2751.

[3]. Xu H, Wang Y, Jian S, et al. Calibrated one-class classification for unsupervised time series anomaly detection[J]. IEEE Transactions on Knowledge and Data Engineering, 2024.
+ TimeInf addresses the gap between existing data contribution methods and the unique requirements of time series data.
+ The proposed influence function is highly versatile, with multiple variants supporting diverse anomaly detection settings. Its model-agnostic nature further enhances its applicability across various models.
+ TimeInf is computationally efficient, leading to significant resource savings.
This work presents TimeInf, a data contribution estimation model for time series. TimeInf overcomes the traditional i.i.d. setting of influence functions, making it more suitable for time series data. By considering multiple time blocks, TimeInf captures contextual information within time series data. Additionally, its model-agnostic design enhances its versatility and flexibility.
+ Some key mathematical terms in the paper could benefit from clearer explanations, such as $\delta_{x}[m]$ and $z^[m]$.
+ The paper lacks a clear mathematical definition of the task, especially regarding the tasks targeted by the variants of TimeInf, which could cause confusion.
+ Although the authors describe TimeInf as a data contribution estimation method, its task definition and benchmark choices make it appear primarily as an anomaly detection model. While data pruning experiments are provided in Appendix Section E, more direct evidence would help demonstrate that TimeInf goes beyond anomaly detection.
+ The comparisons would benefit from including more advanced anomaly detection algorithms [1], [2], [3].
+ In Section 4.3, the authors attribute TimeInf's relatively poor performance in Table 4 to mislabeled ground truth annotations. However, they need to clarify why other benchmark models are unaffected by these mislabeled annotations. Demonstrating that other models do adhere to potentially mislabeled annotations would help validate this claim.
Yes
No ethics review needed.
1.	Can you elaborate on how TimeInf extends beyond the local historical context to capture a more global perspective as mentioned in Section 3?
2.	Following Q1, regarding Table 3, can you provide baseline comparisons to show the model’s advantages in capturing long-term dependencies?
The paper is well-organized with clear problem formulation and concise visualization. It effectively demonstrates the utility of TimeInf across multiple tasks, providing robust results on time-series datasets.
The paper introduces TimeInf, a model-agnostic data contribution estimation method for time-series datasets. It uses influence scores to attribute predictions to individual time points, preserving temporal dependencies. TimeInf shows effectiveness in detecting anomalies, providing interpretable attributions, and identifying mislabeled anomalies in ground truth.
1.	My main concern is that while TimeInf is presented as a general model-agnostic method, the experiments in the main text focus solely on anomaly detection. It would be better to include more different tasks to support the advantage of this general method rather than only elaborate on one task.
2.	Table 2 contains misformatted bold values that do not reflect the best performance (UCR and SMAP’s F1).
3.	The data pruning experiments use non-standard time-series forecasting metrics; it will be better if more common metrics like RMSE and MAE can be considered.
@inproceedings{
anonymous2024timeinf,
title={TimeInf: Time Series Data Contribution via Influence Functions},
author={Anonymous},
booktitle={Submitted to The Thirteenth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=Vz0CWFMPUe},
note={under review}
}
Evaluating the contribution of individual data points to a model's prediction is critical for interpreting model predictions and improving model performance. Existing data contribution methods have been applied to various data types, including tabular data, images, and text; however, their primary focus has been on i.i.d. settings. Despite the pressing need for principled approaches tailored to time series datasets, the problem of estimating data contribution in such settings remains under-explored, possibly due to challenges associated with handling inherent temporal dependencies. This paper introduces TimeInf, a model-agnostic data contribution estimation method for time-series datasets. By leveraging influence scores, TimeInf attributes model predictions to individual time points while preserving temporal structures between the time points. Our empirical results show that TimeInf effectively detects time series anomalies and outperforms existing data attribution techniques as well as state-of-the-art anomaly detection methods. Moreover, TimeInf offers interpretable attributions of data values, allowing us to distinguish diverse anomalous patterns through visualizations. We also showcase a potential application of TimeInf in identifying mislabeled anomalies in the ground truth annotations.
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Time Series Data Contribution Time Series Anomaly Detection
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TimeInf: Time Series Data Contribution via Influence Functions
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