Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 3: reject, not good enough
review_content: summary_of_the_paper: In the paper, the authors proposed a time-series forecasting framework to overcome the distribution shifts and tackle missing values simultaneously. 
strength_and_weaknesses: Strengths
1. An important problem is studied
Weaknesses:
1. Weak motivation for proposed model components
2. Paper presentation and organization need to be improved
clarity,_quality,_novelty_and_reproducibility: This paper is difficult to follow due to the unclear presentation, especially in the model part. Further improvement is needed to improve the clarity. 
summary_of_the_review: In this paper, the authors proposed a novel time series forecasting framework that handles missing data and distribution drift. However, the paper is not clearly presented, and the following issues should be addressed: 

1. The presentation and organization of this paper need to be improved. There are many typos and incomplete sentences. For example, on page 2, "practice, imputation models are first ...". 

2. What's the advantage of inferring the latent variable separately instead of using an encoder? The motivation is not strong here, and the authors didn't provide enough details. Besides, a point-wise distance-based loss function (e.g., MSE) may not be enough to capture the shape correlation between two-time series. Can the authors provide more information and analysis regarding the design of latent vector inference?

3. What's the meaning of s_w / 2 in Figure 1 and equation 7? What is p in equation 7? The authors should clearly describe and explain the equations used in the paper. 

4. How does the imputation work in the inference of latent vectors? Can the authors provide more details?
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: In this paper, authors proposed a multivariate time-series forecasting model (SpectraNet) that unified the forecasting and interpolation problem. Specifically, the model first infers the optimal latent vector on the reference window by minimizing the reconstruction error, then the model generates the full predictions via a latent space spectral decomposition module. The proposed model achieves the best performance compared with other existing methods.

strength_and_weaknesses: **Strengths**:  
1. Well-organized and clearly written.  
2. Promising results.  


**Weaknesses**:  
1.  In Sec. 3.5, the distribution shift is defined as the difference of missing data regime between training set and test set. However, in my opinion, this kind of difference is not the distribution shift, since the training and test sets both come from the **same** dataset in a random split (or not) manner, the **data distribution** should be the same in the training and test sets, even though the total numbers or locations of missing values are different. Therefore, I would say there is no distribution shift problem.

2. Some key details are missing.   
(a) In Sec. 3.2, how many temporal bases $B$ are used? What's the insights or reasons?   
(b) In Sec. 3.3, there is no clarification of the ConvTranspose1d, more details should be included. Why do the first two layers learn a common representation and the second layer refine the temporal resolution? There is no such experiment or explanation of this claim. In addition, the *causality* is not clear either, "the latent vector $z^{*}$ is only inferred with information on the reference window" is not the reason of  *causality*.  
(c) In Sec. 4.3, it says "all models are trained with the training loss only on available values", how about the missing points? I think the ground truth of missing points is accessible during training, if the model doesn't use the missing points during training, what's the meaning of interpolation?  



3. Experiments are not sufficient. There is no ablation study to demonstrate the effectiveness of some designs in the model, i.e., temporal basis, the inference step, etc.


4. Minor mistakes:  
(1) In Sec. 3.1, the first sentence is incoherent, "of the", "instead of".  
(2) In Fig. 2, the legend blocks the first curve $\hat{y_{1}}$,  even though it looks the same as $\hat{y_{10}}$ . Almost the same problem in all the figures.  
(3) Eq. (8), not aligned.  
(4) In Fig.3, the characters are too small.  
(5) In References, the names of conferences or journals, i.e. AAAI or AAAI Press , are not consistent.  
I highly encourage authors to revise the submission to avoid such small mistakes, as well as some typos.  


5. Some missing references[1,2] when addressing distribution shift problem in time-series.  
[1] Adaptive Trajectory Prediction via Transferable GNN. CVPR2022  
[2] Expanding the Deployment Envelope of Behavior Prediction via Adaptive Meta-Learning. arXiv 2022




clarity,_quality,_novelty_and_reproducibility: Details are in [Weaknesses]

**Clarity**:  
The clarity is good but with some minor mistakes.

**Quality**:  
Clear-written and well-organized.

**Novelty**:  
Motivation is good but the contributions are not significant.

**Reproducibility**:  
The training procedure is clear in Appendix 5,  and authors promise to release the code after paper acceptance. 

summary_of_the_review: I list my concerns in [Weaknesses], I am happy to discuss and increase the rating if my concerns are addressed.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: To tackle the distribution shift and missing data problem of time series, this paper proposes a latent space spectral decomposition method for simultaneous time series forecasting and imputation. The latent vector is optimized individually for unseen data and thus can generalize well to unseen data distribution. 
strength_and_weaknesses: Pros:
1) The idea to optimize a latent vector for different data is interesting and this is the first time this idea is applied on time series. Previously this idea has been used to images [2]. 
2) Experiments result are better than several baselines

Cons: 
1) The idea to combine several basis functions to reconstruct the input is not new. Previously, [1,3] used this idea to reconstruct music signals. Also, I am not sure that only using sin, cos, and poly functions are enough for all types of time series datasets. Some datasets may have strange shapes that can not be reconstructed well.
2) For optimization, I am not sure about using the inference step and the learning step can lead to a globally optimal solution. It would be great if the authors can provide some explanation here. 

[1] DDSP: Differentiable Digital Signal Processing
[2] Optimizing the Latent Space of Generative Networks 
[3] Differentiable Wavetable Synthesis
clarity,_quality,_novelty_and_reproducibility: Clarity: Good
Quality: Good
Novelty: Good
Reproducibility:Good
summary_of_the_review: Despite the drawbacks that I mentioned, I think this is an interesting paper overall.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: The paper proposes SpectraNet that can simultaneously produce forecasts and interpolate past observations. The method achieves some good overall performance. 

Two reviewers do not support the publication of this paper at ICLR. After reviewing and considering carefully, I also think that the paper is not ready for the publication. 

1) The idea to combine several basis functions to reconstruct the input is not new. The authors explain that this paper uses the basis as a latent representation which is different. However, this is not really significant novel in terms of contributions. 
2) The authors mentioned that for optimization gradient descent on non-convex objectives could guarantee to converge to the global optima. This is generally not true since there is no rigorous work that can show convergence to global optimal solution in the deep learning applications. 
3) The comparison to the previous work may not be fair. The authors did not mention about training epochs (I see 500 and 1000 in appendix) and I wonder if it is a fair comparison with the previous work. In Autoformer paper, their training process is early stopped within 10 epochs. 
4) The experimental results seem skeptical since the authors do not provide the comparison with some latest state-of-the-art method such as in Zeng et al. “Are Transformers Effective for Time Series Forecasting?”. Moreover, the numbers in the tables seem quite different. 
5) There is no code to reproduce results. Therefore, it is hard to justify the effectiveness of the methods. 

The results may be promising but not clear if it is a fair comparison or not. 

justification_for_why_not_higher_score: - The idea to combine several basis functions to reconstruct the input is not new. 
- Gradient descent on non-convex objectives could not guarantee to converge to the global optima. 
- The comparison to the previous work may not be fair.
Decision: Reject