iHyperTime: Interpretable Time Series Generation with Implicit Neural Representations

Weaknesses

We thank the reviewer for their comments and suggestions. We hope they find our answers useful, and we are happy to answer any additional questions.

W.1.

We apologize for the lack of clarity in the description of the method. TSNet uses a SIREN to model the Residual component, and a Fourier decomposition to model the Seasonality component. We do not actually use a Fourier mapped perceptron (FMP), and we corrected the related section. In particular, we have rewritten all Section 3.1.1 to provide a more concise and clear explanation of the TSNet architecture.

W.2.

We thank the reviewer for raising this question. If f(t) is multidimensional, iHT models each dimension as $f_T(t) + f_S(t) + f_R(t)$ independently. Following an $m$-dimensional time series, the trend block outputs $m$ trends, the seasonality block outputs $m$ time series that correspond to the seasonality of each feature, and the same is for the residual block. Each of the features are then added together obtaining an $m$-dimensional time series.

W.3.

We apologize for the lack of clarity in the description of the generation mechanism. The model does require samples of time series to generate a new one. Generation of new time series is produced by randomly selecting pairs of time series, and performing linear a interpolation between their embeddings $Z^{(1)}$ and $Z^{(2)}$:

where $\\lambda$ is also sampled randomly. Optionally, the interpolation can be performed on individual components $Z_T$, $Z_S$, $Z_R$ of the embeddings, enabling the conditional generation of time series. 

In the current setting the model cannot synthesize new samples without {t, f(t)}. This could be achieved in a variational setting or by incorporating adversarial training, which we plan for a future work. We have now refactored Section 3.2 of the main paper to include more details on the generative process.

W.4.

We thank the reviewer for the suggested reference, we have now cited Deep Sets in the revised paper version, in the set encoder subsection in Section 3.2.

Minor Weaknesses

MW1 /. Q.4.

We have now revised Section 3.1.1 to clarify and remove any misleading statements about SIREN outperforming Fourier Features Networks (FFNs) in terms of spectral bias. Following Q4, we will provide an ablation study shortly comparing SIREN and FFN and will add a more extensive discussion in the final version of the paper.
[UPDATE] We have added the additional ablation studies in the supplementary material, and we discuss them in a comment below.

MW2

We acknowledge that Figure 4 is missing essential details and a more accurate discussion of the results. We also agree with the reviewer that the main goal of our analysis is showing a relatively low computational time for our approach w.r.t. existing methods, as also shown in Table 12. In re-writing the final paper, we are making sure of not claiming any independence with respect to the sequence length.

More details Our experiments use the same synthetic data-set of 8192000 data-points (e.g. number of samples $\times$ sequence length), organized in 5 datasets of different sequence lengths $l \\in \\{80, 320, 1280, 5120, 20480\\}$. Thus, we obtain 5 datasets of $\\{102400, 25600, 6400, 1600, 400\\}$ number of samples, which we process using $\\{1024, 256, 64, 16, 4\\}$ as batch-size, respectively. Thanks to this batch-size, we can fairly train each model for 100 iteration and always loading to GPU the same amount of data-points, for each sequence length and iteration.For inference, we only sample a single batch of data.

Impact of data loading All the times are computed directly in the training and testing loop, after the model has been already loaded in the GPU memory, using a NVIDIA T4 GPU. Moreover, we found that the data loading (both for training and inference) is negligible w.r.t. model computational time. We measure the loading being around $0.0145$ sec for training (100 iterations) and inference $0.001$ sec (1 epoch).

Fourier Flow Finally, we repeated the experiments with Fourier Flows with the new computational times reported in Table 2 of supplementary. However, we still have some convexing. We believe the slightly drop likely comes from not optimized code to handle large batch-sizes: longer time-series (e.g., 320 and 1280) worsen the computational time, but the model is also relieved by the smaller batch-size (e.g., 256 and 64).

MW3

We thank the reviewer for spotting this issue. We are improving the charts in the final version of the paper with the same scale for both the x and y axes. Figure 5 of the supplementary material already shows some of the new charts.

MW4

We apologize for the lack of clarity in the description of the method. We are incorporating a new detailed description of our time series generation procedure.

MW5 / W.3 / Q.3.

We thank the reviewer for the suggestion.

Reconstruction. In the supplementary material we now report both the quantitative and qualitative metrics to assess the quality of the reconstruction in train and test set. In Table 5 of supplementary we report the reconstruction error for the iHyperTime for the Energy24, Stock24, Stock72, and Stock360 datasets. While Figure 6 and Figure 7 show the actually quality of reconstructed time-series for Stock 72 and Stock 360, respectively.

Latent dimension The model results at varying of the latent dimensions $Z_T$, $Z_S$ and $Z_R$ are shown in the supplementary material on Table 3 and Table 4 for stock 24 and stock 72, respectively. As suggested we evaluate both the reconstruction error and the generation metrics, for different z_{T}_{S}_{R} values (e.g., z_4_6_8 represents $Z_T=4$, $Z_S=6$ and $Z_R=8$). The results show comparable results for Stock 72. For Stock 24 we have slightly better generative performance for small dimensions at the cost of higher reconstruction error, and vice versa.

Other Questions

Q.5.

In Table 5 of supplementary we report quantitative metrics to evaluate the reconstruction quality using iHyperTime for Energy24, Stock24, Stock72, and Stock360 datasets. Figure 6 and Figure 7 report the qualitative results, showing the reconstructed time-series for Stock 72 and Stock 360, respectively.

Q.6.

We apologize for not introducing the Marginal Score for all the datasets. For simplicity, for each dataset we decided to use only the most common metrics used in the related benchmark papers. Therefore, only Monash uses the marginal score[1]. In our current effort we are in integrating Marginal score also for the other datasets. Table 1 of supplementary material shows the marginal score results for Stock 24.

[1] - Zhou, Linqi, et al. "Deep latent state space models for time-series generation." International Conference on Machine Learning. PMLR, 2023.

We would like to sincerely thank the reviewer for their effort and interesting comments. We now included an additional supplementary material along the main paper. The supplementary contains our new experiments to address reviewer's concerns.

Major Weaknesses

W.1. / Q.1.

In Figure 1 and Figure 2 we show the reconstructed time-series from interpolations between pairs of embeddings generated by our architecture on the Stock72 dataset, and Figures 3 and 4 correspond to the Stock 360 dataset. The figures show the time-series reconstruction and the embeddings interpolation for a given latent vector z1 and another latent vector z2, at varying $\lambda \in [0, \ldots, 1]$ (as requested in Q.1).

In the top row, we show a smooth transition from $z_1$ to $z_2$, in terms of the fully reconstructed time series. Our architecture also performs a TSR decomposition of the time series, and hence in the three bottom rows we display the smooth transition between $z_1$ and $z_2$ of each individual component of the time series (Trend, Seasonality, Residual).

We will add these plots in the main paper. We better discuss the diversity of generated time-series in the next comment.

W.2. / Q.2.

Train-Test Split. We agree that splitting the time series into train/test is the best approach for a fair evaluation of the generative models. However, we found that some of state-of-art approaches train and test the model on the whole dataset for Stock and Energy data[1,2,3]; and to perform a consistent comparison w.r.t. the performance reported in their original paper, we decided to keep the same approach in our paper. We however agree with the reviewer's concern, and thus we are happy to report in the table below (also Table 1 of supplementary) our initial effort in evaluating approaches while randomly splitting data between training set (i.e., 80$\\%$ of dataset) and test set (i.e., 20$\\%$ of dataset). The Table reports the quantitative metrics for the regular Stock data with length 24. While Figure 5 in the supplementary material shows the t-SNE visualization and the data distribution. These results confirm the findings from the our paper. Notice that, for the Monash datasets we already divided the dataset in training ($80\%$) and test ($20\%$) set, similar to the benchmark model LS4 [4].

Diversity. Finally, we also agree that diversity of generated time-series plays a key role in the evaluation of generative models. We can qualitatively evaluate the diversity and coverage from t-SNE of Figure 5 (as well as in t-SNE plots of the main paper). The t-SNE plots show that iHyperTime synthetic data mostly overlap with real data: i.e., iHyperTime is able to have enough diversity to reconstruct the real data distribution. Following reviewer suggestion, we also use a novel metric to quantitatively evaluate the diversity of time-series, namely $sym$-Recall[6] which extends the $\\beta$-Recall from[5]. Such metric quantifies the diversity of time-series as the extent to which synthetic samples cover the full variability of real samples. Initial results are reported in the Table below.

\\begin{array}{l|ccccccc} \\hline \\text{Metric} & \\text{iHT (Ours)} & \\text{GT-GAN} & \\text{TimeGAN} & \\text{DiffTime} & \\text{LS4} & \\text{FFlows} \\\\ \\hline \\text{Discr-score} \\downarrow & 0.054\\pm0.028 & 0.273\\pm0.046 & 0.068\\pm0.018 & 0.079\\pm0.014 & 0.154\\pm0.080 & 0.426\\pm0.032 \\\\ \\text{Pred-score} \\downarrow & 0.037\\pm0.000 & 0.046\\pm0.001 & 0.043\\pm0.001& 0.044\\pm0.001 & 0.039\\pm0.000 & 0.055\\pm0.003 \\\\ \\text{Marginal Score} \\downarrow & 0.355 & 0.403 & 0.434 & 0.359 & 0.513 & 0.335 \\\\ \\text{sym-Recall} \\uparrow & 0.594 & 0.500 & 0.413 & 0.787 & 0.206 & 0.000 \\\\ \\hline \\end{array}

We will add a more extensive discussion, and new experiments in the final version of the paper.

References

[1] - Yoon, Jinsung, Daniel Jarrett, and Mihaela Van der Schaar. "Time-series generative adversarial networks." Advances in neural information processing systems 32 (2019).

[2] - Jeon, Jinsung, et al. "GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networks." Advances in Neural Information Processing Systems 35 (2022): 36999-37010.

[3] - Alaa, Ahmed, Alex James Chan, and Mihaela van der Schaar. "Generative time-series modeling with fourier flows." International Conference on Learning Representations. 2020.

[4] - Zhou, Linqi, et al. "Deep latent state space models for time-series generation." International Conference on Machine Learning. PMLR, 2023.

[5] - Alaa, Ahmed, et al. "How faithful is your synthetic data? sample-level metrics for evaluating and auditing generative models." International Conference on Machine Learning. PMLR, 2022.

[6] - Khayatkhoei, Mahyar, and Wael AbdAlmageed. "Emergent Asymmetry of Precision and Recall for Measuring Fidelity and Diversity of Generative Models in High Dimensions." arXiv preprint arXiv:2306.09618 (2023).

Other Questions

Q.7.

Temp Rain. The Temp Rain dataset has more complex temporal dynamics, which make the generative process more difficult. In particular, Temp Rain data has stiff transitions: i.e., most of the data points lie around on the x-axis (y=0) with very sharp spikes [1]. Therefore, a model could achieve very low marginal score by just generating data closely to the x-axis. Such data however are also easily distinguishable from the real data, for a good predictive model. Therefore, we believe LS4[2] generates good data, but with less sharp spikes than the real data, achieving better marginal score but lower Classification score w.r.t. our approach. This would also explain the high predictive score in LS4, where less sharp spikes would also hinder the predictive power of a model trained on synthetic data but tested on real.

We will add more detailed discussion in the final version of the paper.

Notation. Regarding the different notations for the metrics in Tables 1-4 and Table 5, in order to make a fair comparison with the state-of-the-art benchmarks, Tables 1-4 follow the predictive and discriminative scores as they are set up in TimeGAN, GT-GAN, DiffTime, etc, whilst in Table 5 we follow the same set up for Classification and predictive score as LS4. Moreover, in Table 5 we show results in the Monash dataset, where three of the datasets have time series with sequence length greater than 700. Given that the predictive and discriminative scores in Tables 1-4 are RNN-based, the time to compute the metrics would be impractical. In addition, the RNN-based metrics might not be able to capture the more complex dynamics from the Monash datasets.

[1] - Temperature Rain Dataset without Missing Values, https://zenodo.org/records/5129091

[2] - Zhou, Linqi, et al. "Deep latent state space models for time-series generation." International Conference on Machine Learning. PMLR, 2023.

Q.8. and Q.9.

We thank the reviewer for the good suggestion. We are actually training DiffTime for Monash, which we initially omitted due to the longer training times. We also agree that the performance seems to have an anomaly for 30 Stock missing data. We will add the new results soon, and we will integrate them in the final version of the paper.

Q.4

We appreciate the reviewer's suggestion for these important ablation studies. We have included both analyses in the supplementary material, and discuss them below. We will include these additional results in the final version of the paper.

Analysis of $w_0$. In Section 1.7 of the supplementary material, we have included the performance of iHT using different values of $w_0$ in the SIREN layers. In the Tables A and B below, we report the reconstruction and generation metrics for the Stock24 and Stock72 datasets. In Stock24, the best reconstruction and generation metrics are obtained with $w_0=30$. In the case of Stock72, the best reconstruction metric is also obtained with $w_0=30$, but the discriminative and predictive scores show a slight improvement for $w_0=100$.

Table A: Results for iHT with different values of $w_0$ for the Stock24 dataset.

Table B: Results for iHT with different values of $w_0$ for the Stock72 dataset.

Comparison with FFN. In Section 1.8 of the supplementary material, we now report the performance of a variant of iHT that uses Random Fourier Features (FFN) instead of SIREN for the representation of residuals. Given the importance of the scale factor in FFN as explained in [1], we evaluated FFN with multiple scale factor values: 5, 10, 100. The Tables C and D below show the reconstruction and generation metrics for the Stock24 and Stock72 datasets, respectively. For the Stock24 dataset, SIREN achieves the best reconstruction performance as well as the lowest discriminative score. In the case of Stock72, FFN with scale factor 10 achieves better reconstruction errors, and shows slightly better performance in discriminative score than SIREN network.

Table C: Results for with SIREN layers and with FFN for Stock24 dataset.

Table D: Results for with SIREN layers and with FFN for Stock72 dataset.

[1] Woo, Gerald et al. “Learning Deep Time-index Models for Time Series Forecasting.” International Conference on Machine Learning (2022).

We thank the reviewer for the suggestions. We acknowledge that the paper presentation was not clear enough. In the new version of the paper we extensively rewrite section 3, and we have colored the rewritten parts in blue to highlight the modifications/additions. As suggested, we have also evaluated our approach on three real datasets, showing that the model is able to disambiguate between season, trend, and residual in an interpretable manner for real world data.

I hope the reviewer finds our results useful in assessing the quality of our work. We are happy to answer any additional questions.

Weaknesses

W.1

We apologize for the lack of clarity in the description of the generative method. In the main paper we have now added a subsection at the end of section 3.2 explaining how we perform generation. Generation of new time series is produced by randomly selecting pairs of time series from the training-set, and performing a linear interpolation between their embeddings $Z^{(1)}$ and $Z^{(2)}$: $Z^{\\text{gen}} = Z^{(1)} + \\lambda (Z^{(2)} - Z^{(1)})$ where $\\lambda$ is also sampled randomly. Optionally, the interpolation can be performed on individual components $Z_T$, $Z_S$, $Z_R$ of the embeddings, enabling the conditional generation of time series.

W.2

We apologize for the mistake in explaination of the seasonal component: when we said "seasonal" we should have said "residual".

Change of notation In the trend and seasonality networks, we used $t$ because there is a single layer. And in residual, we used $x$ to indicate the outputs of the successive layers. We should have clarified this, also stating that $x_0 = t$. We have now rewritten this section ensuring consistency of the notation.

Random Fourier Features We apologize for the lack of clarity in this aspect. Our initial goal was to convey that using SIRENs or random Fourier Features was equivalent w.r.t. having a good representation of frequencies in the signal, following [1]. However, we agree that this leads to confusion. We have now revised Section 3.1.1 to clarify this and we removed any misleading statements about Fourier Features Networks (FFNs).

[1] Benbarka, Nuri et al. “Seeing Implicit Neural Representations as Fourier Series.” 2022 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) (2021).

W.3

We thank the reviewer for pointing out an important missing aspect. We have now included two subsections in Section 3.2 detailing how the set encoder and hypernetworks are used. For the Set encoder we have provided a mathematical description and how it is parameterized using SIREN layers. We have provided implementation details in Section D.2 of the appendix, which is now referred in the main paper. Furthermore, in section D.2 we have also added more information on how the Set Encoder is used, and provided more details about the hypernetwork architecture.

W.4.

We thank the reviewer for pointing out aspects that were not clearly explained in the paper.

Time coordinate. In our model, we use a single floating point value as temporal coordinate (time $t$). As data pre-processing, all the values are scaled to the interval $[-1, 1]$, with a common global factor for all time series of a dataset. In all cases, regardless of sequence length, the time series is fed to the set encoder as a single set, and is hence converted into a single embedding $Z$. We have now included this information in Appendix D.2.

Datasets. Following previous methods [1, 2, 3], we used the Stock and Energy datasets [5] sliced into 24 time-steps windows. These datasets are multivariate, with 6 and 28 features, respectively. Furthermore, in order to make a fair comparison with [3] and [4], who show performances in longer time series of Stock data, we generated an univariate version of the Stock dataset by selecting one single feature (Close Price), and slicing it in two ways: using a window of 72 time steps (Stock72), and a window of 360 time steps (Stock 360).

Additionally, in Section 4.4 we consider 4 univariate datasets with longer real-world time-series from Monash repository [6], namely FRED-MD, NN5 Daily, Temperature Rain, and Solar Weekly. The first three datasets have time series of approx. $750$ time steps, while the last one contains time series of length $52$. This information is summarized in Appendix B, where Table 8 presents the main characteristics of each dataset. We have improved this table to clarify the difference between the different datasets, in terms of sequence length and number of channels. And we refer this table in Section 4.1 of the main paper.

Finally, in Section 4.3 we evaluate our method on irregular data. Following existing literature [2], we create irregular time-series datasets by randomly dropping 30, 50, 70% of observations from the original datasets. We select each observation to drop uniformly at random, and independently for each time series $\{(t_i, y_i)\}_{i=0}^N$ in the original dataset.

• [1] J. Yoon, D. Jarrett, M. van der Schaar. Time-series generative adversarial networks. In NeurIPS, 2019.

• [2] J. Jeon, J. Kim, H. Song, S. Cho, N. Park. GT-GAN: General purpose time series synthesis with generative adversarial networks. In NeurIPS, 2022.

• [3] A. Coletta, S. Gopalakrishan, D. Borrajo, S. Vyetrenko. On the constrained time-series generation problem. In NeurIPS, 2023.

• [4] A. Alaa, A. Chan, M. van der Schaar. Generative time-series modeling with fourier flows. In ICLR, 2021.

• [5] L. Candanedo, V. Feldheim, D. Deramaix. Data driven prediction models of energy use of appliances in a low-energy house. Energy and buildings, 140:81–97, 2017.

• [6] R. Godahewa, C. Bergmeir, G. Webb, R. Hyndman, P. Montero-Manso. Monash time series forecasting archive. In NeurIPS, 2021.

Questions

Q.1

We thank the reviewer for suggesting an interesting new experiment. We have now conducted an analysis on three real world datasets to show that iHT is able to disambiguate between trend, season and residual components after training.

The new experiments are included in Section 1.6 of a new supplementary material, submitted along the main paper. We will add the experiments in the final version of the paper.

Datasets

We used two well known real-world time series datasets that exhibit strong seasonality and trend: Atmospheric CO2 and Airline Passenger, and used the Stock72 dataset described in section B of the supplementary material that exhibits strong trend but low seasonality.

The Atmospheric CO2 dataset corresponds to monthly data (January 1959 to December 1987) with a total of 348 observations with a seasonality period of 12 [1]. We sliced the data into time series of sequence length 60, obtaining a total of 288 time series.

The Airline Passenger dataset corresponds to monthly data (January 1948 to December 1960) with a total of 144 observations with a seasonality period of 12 [2]. We sliced the data into time series of sequence length 36, obtaining a total of 108 time series.

To estimate the presence of trend and seasonality of each dataset we use two metrics defined in [3]: the strength of trend and strength of seasonality. As these datasets do not include ground-truth trend and seasonality, we estimate them using STL [1]. Given a time series with additive decomposition in trend, seasonality and residual: $y_t = T_t+ S_t + R_t$ , we can define the strength of trend as:

This measures the relative variance of the residual component $R_t$ to the variance of the trend with the residual component. The value ranges from 0 to 1, with 0 indicating no trend and 1 indicating a strong trend.

Strength of seasonality is defined by:

Which measures the relative variance of the residual component $R_t$ to the variance of the seasonality with the residual component. A value close to 0 indicates little to no seasonality, and a value close to 1 indicates strong seasonality.

Table below shows these metrics for the three datasets. As expected, Stock72 doesn't exhibit strong seasonality (as stock data usually have not such component), while the other two datasets exhibit strong trends and seasonality, with all values on average above 0.98.

Results

We trained iHT on each dataset and we show in Figures 8 and 9 of the Supplementary the reconstructed time series and the output of each of the individual blocks for the CO2 and Air Passanger datasets, respectively. For the output of the trend, seasonality and residual block, we compare with the STL method. We observe that there is a good agreement in the trend and seasonality components in both datasets. The STL method requires as parameter the period of the seasonality, which is known for both datasets, while our approach is able to estimate the seasonality from the data. In the case of the Stock72 dataset, for the STL comparison, we estimated the period using a Fourier transform and retrieving the dominant frequency. Figure 10 of the supplementary shows the decomposition generated by iHT and compared against STL. We can see in this case that the seasonal component is quite small in magnitude compared to the residuals.

We will include this new analysis on real-world data in the revised version of the manuscript.

[1] Cleveland, R. B., Cleveland, W. S., McRae, J. E. & Terpenning, I. (1990). STL: A Seasonal-Trend Decomposition Procedure Based on Loess (with Discussion). Journal of Official Statistics.

[2] Downloaded from https://www.kaggle.com/datasets/rakannimer/air-passengers

[3] Wang, X., Smith, K. A., & Hyndman, R. J. (2006). Characteristic-based clustering for time series data. Data Mining and Knowledge Discovery, 13(3), 335–364.

Thanks for the extensive response. I have raised my score since my queries have been addressed, and I think this work introduces a novel method with good performance.

However I do have a few comments:

1. Section 3.2 is titled "TIME SERIES GENERATION WITH IHYPERTIME" but is still addressing architecture and training, only addressing generation in the last paragraph. This section/title should be changed to something more appropriate.
2. It turns out the model can only do conditional generation. This was not explained in the original manuscript, and in the updated manuscript, it is only mentioned once in the middle - this needs to be highlighted more clearly in the introduction, and preferably the abstract as well.
3. Furthermore, it is clear that the proposed method would outperform baselines on the evaluation metrics being used, due to the fact that it is a conditional generation method. This should be highlighted in a limitations section.

We thank the reviewer for pointing out aspects that were not clearly explained and discussed in the paper.

Weaknesses:

W1

Following existing literature [1,2,3] we create irregular time-series datasets by randomly dropping 30, 50, 70% of observations from the original datasets. We select each observation to drop uniformly at random, and independently for each time series {$(t_i, y_i)$}$_{i=0}^N$ in the original dataset. The randomly removed data is the same for every model and every repeat, and used both in training and testing. We will add citations and more details for the irregular time-series dataset generation in the final version of the paper.

W2

We thank the reviewer for pointing out two interesting tasks that were not sufficiently discussed. While our work primarily focuses on learning an interpretable trend-seasonality time series representation for time-series generation, we agree with the reviewer that this latent representation could be easily used and leveraged in broader applications, like cluster or classification. In particular, these applications could extensively benefit from the learned interpretable decomposition that separates trend, seasonality and residuals. We will discuss the possible different applications in the final version of the paper.

W3

We thank the reviewer for the suggestion. In our current effort, we are improving the state-of-art section discussing related GNN work [4,5,6,7]. Among this work we note that:

• the work in [4] is the only one directly addressing the generation of time-series using a Graph-based model. Although contemporaneous, we plan to compare our proposed approach against this model, and we contacted the authors to access their code.

• the work in [5] proposes an interesting graph neural network approach to embed irregularly sampled and multivariate time-series. While the work focuses on forecasting, it can be extended to other applications including generation. We are evaluating the complexity and effort of adapting such model for a comparison.

References:

[1] - Jeon, Jinsung, et al. "GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networks." Advances in Neural Information Processing Systems 35 (2022): 36999-37010.

[2] - Kidger, Patrick, et al. "Neural controlled differential equations for irregular time series." Advances in Neural Information Processing Systems 33 (2020): 6696-6707.

[3] - Tang, Xianfeng, et al. "Joint modeling of local and global temporal dynamics for multivariate time series forecasting with missing values." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 34. No. 04. 2020.

[4] - Iyer, Srikrishna, and Teng Teck Hou. "GAT-GAN: A Graph-Attention-based Time-Series Generative Adversarial Network." arXiv preprint arXiv:2306.01999 (2023).

[5] -Zhang, Xiang, et al. "Graph-Guided Network for Irregularly Sampled Multivariate Time Series." International Conference on Learning Representations. 2022.

[6] - Andrea, Cini, Marisca Ivan, and Cesare Alippi. "Filling the Gaps: Multivariate Time Series Imputation by Graph Neural Networks." ICLR 2022. 2021. 1-20.

[7] - Jin, Ming, et al. "A survey on graph neural networks for time series: Forecasting, classification, imputation, and anomaly detection." arXiv preprint arXiv:2307.03759 (2023).

I would like to thank the authors for clarifying the weaknesses and questions that I have raised. While W1 & W2 have been addressed by the authors, W3 and Q1 remain to be a concern since comparison appears to lack important methods/baselines.