HDDI: A Historical Data-Based Diffusion Imputation Method for High-Accuracy Recovery in Multivariate Time Series with High Missing Rate and Long-Term Gap

• The literature review appears fairly up-to-date, yet there is a notable absence regarding diffusion models for imputation: PriSTI [1]. Is there a particular reason for its omission?

• The paper discusses GRIN [2], which demonstrates the need for imputing by extracting spatio-temporal representations through GNNs. This approach appears beneficial in cases with extended missing data periods, including virtual missing experiments where imputations are made in scenarios where a node has failed across all training samples, showing notable improvements. PriSTI iterates on CSDI [3] by integrating GNNs, among other features, to leverage these advantages. Is there any reason GNNs were not considered in this paper? This method seems potentially beneficial to the proposed approach.

• The method of matching records from historical data is quite interesting, but it appears that this approach could scale linearly in complexity as new records are added in production. This raises the following questions: Do you have any analysis on how complexity grows under this scenario? Are there any constraints in place to mitigate this, such as limiting the maximum time window considered?

• Lines 60–63 mention that diffusion models can avoid the error accumulation problem of RNNs. However, this seems to be a minor error, as specified in [1, 3], and as noted in lines 117–121 of this paper, this issue is actually mitigated by self-attention methods incorporated within transformer layers. This confusion appears again in lines 47–50, where it seems to imply that error accumulation is linked to self-attention mechanisms. Is this correct, or is there a misinterpretation on my part?

• Another potential source of confusion is the use of the terms "forward process" and "denoising process." The diffusion process specifically refers to adding noise to a sample, while the denoising process is the mechanism for reconstructing the original sample from the noise, which is the primary task we aim to teach diffusion models. During training, both the diffusion process and the denoising task are involved. However, in lines 101–103, the text seems to imply that the forward process refers to model training, and that denoising corresponds to inference. Could this be a minor error, or is there a misinterpretation on my part?

• Finally, the approach of searching for historical values for missing data recalls PriSTI’s method of providing diffusion models with linearly interpolated imputed data to serve as conditional information [1]. Has the similarity been explored in this context?

[1] Liu, M., Huang, H., Feng, H., Sun, L., Du, B., & Fu, Y. (2023, April). Pristi: A conditional diffusion framework for spatiotemporal imputation. In 2023 IEEE 39th International Conference on Data Engineering (ICDE) (pp. 1927-1939). IEEE.

[2] Cini, A., Marisca, I., & Alippi, C. (2021). Filling the g_ap_s: Multivariate time series imputation by graph neural networks. arXiv preprint arXiv:2108.00298.

[3] Tashiro, Y., Song, J., Song, Y., & Ermon, S. (2021). Csdi: Conditional score-based diffusion models for probabilistic time series imputation. Advances in Neural Information Processing Systems, 34, 24804-24816.

1. In my opinion, the use of sliding windows for matching historical data may present significant computational challenges, especially with large datasets or those sampled at high frequencies. Could the authors discuss their approach to selecting the optimal sliding window length and how this affect the efficency of the HDDI?

2. Following the previous question, could the authors provide a detailed complexity analysis of the HDDI pipeline? This would be useful to understand real-time feasibility in large-scale data applications.

3. In Appendix 7.3, the baseline methods section considers only five methods, most of which are from pre-2021. Including a broader range of state-of-the-art methods would strengthen the comparison, for instance, TimesNet and iTransformer.

4. In Appendix 7.3's missing data scenarios section, the methodology for generating LM scenariosis not clear to me. The authors mention selecting damaged features and removing points from these features. Does this imply that remaining features are fully observed while all points in damaged features are removed?

As in weaknesses.

1. Did the hyperparameters of the baseline models get optimized? If so, please provide the details of the experiments regarding this point.
2. I didn't see baseline models in the code repository. I would like to learn about how the authors reproduced the baseline methods. Using their official code or other unified Python libraries (e.g. PyPOTS, Time-Series-Library)? It is important because data processing is quite different across imputation algorithms (their own implementations), while unified interfaces can ensure fairness in the experiments.
3. All experimental results are averaged over five trials. But why the standard deviation is missing? It is also a vital argument to evaluate the models;

Additional suggestions:

1. To improve the reproducibility of your results, please also list the configuration details of your development environment, e.g. Python package versions, which are missing in the provided code repository;
2. There is only one dataset processing script (i.e. Air Quality) in your code base. It would be better to share all of them to ensure the reproducibility;