Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: In this paper, the authors propose an interpretable spatio-temporal forecasting method by learning shape functions from data. The shape function is designed as a function of the distance between pairwise locations, which is then used to represent the vector autoregressive model coefficients. As a result, the proposed model can incorporate both spatial and temporal information. Furthermore, the interactions between different locations can be interpreted by the shape function outputs, and a graph can be used to visualize the interactions. Finally, the proposed method also achieves promising forecasting performance compared to deep learning methods.
strengths_and_weaknesses: Strength:
The work is well motivated by the challenge in spatio-temporal forecasting, i.e., the tradeoff between accuracy and interpretability. The proposed method uses shape functions to constrain the statistical relations between different locations and achieves good forecasting performance. Overall, I think the paper makes a good contribution to spatio-temporal forecasting.

The explanation of relations to previous works is clear. The proposed method is an extension of traditional methods by replacing the predefined spatial functions with learnable shape functions. The proposed method enjoys good forecasting accuracy as deep learning methods, while maintaining the interpretability of traditional methods.

Weakness:
The main assumption of this paper is the correlation between two locations decreasing with distance. While this assumption may make sense in some applications, it would be better to give some discussions or case studies of this assumption.

In the nonstationary setting, the model in Eq (2) has a different weight matrix for each time step. It seems to be that this design suffers from the small sample problem, as the data at each time step is limited. This would cause fluctuations in the estimations across time. 

In section 3.4, the authors give examples of monotonically increasing/deceasing functions. However, in the experiments, only monotonically decreasing functions are investigated. If increasing functions are not going to be used in the forecast model, it might be better not to mention it the method section.
questions: Questions:
In Eq (1), the authors only consider time lagged correlations. Is it possible to incorporate instantaneous relations at the same time step? The reason why I ask this question is because there might exist instantaneous relations in some applications.

What is the motivation behind the choice of specifications in section 3.2? Are the authors trying to mimic some properties in the classical statistical methods?
limitations: The authors addressed the limitations.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This manuscript focuses on the patio-temporal forecasting problem and proposes a new method with shape functions toward a learnable and explainable model. The proposed method extends the statistical models via learnable bash shape functions, making it possible to capture the spatial variability and distance-based effects over distance. The proposed method is evaluated on both real and synthetic datasets.
strengths_and_weaknesses: Pros:

- The idea of modeling the spatial weight matrix with learnable shape functions is novel and interesting. It generalizes the traditional statistical method by introducing more learnable components.

- Experimental results on both synthetic and real datasets indeed show the effectiveness of the proposed method. It even performs better or is comparable with respect to some DNN-based methods under some scenarios.

Cons:

- The proposed method is only evaluated on a single real-world dataset, making it hard to figure out if the method can consistently work well under real setups.

- The authors provide several specifications of the relations between the distance and the weights. However, the authors did not discuss the advantage or disadvantages of each specification. On a given dataset, how should we choose among them?

- According to section 3.4, the basis function for the shape constraints is simple. There is no discussion about some more complex functions and their influences on the performances. 

Minor issues:

- "modelling" should be "modeling"

- The citation format is a little strange with semicolons and parentheses, it is better to reformat them.

- For better visualization, it is highly recommended to adopt vector graphics for all figures.
questions: - It would be interesting to add more discussion about complex shape functions.

- For the evaluation, it is also suggested to add the inference time beyond the training time, which is more important in real scenarios.

limitations: Yes
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: The paper proposes a spatio-temporal prediction model that tries to incorporate a varying strength of spatial dependency over distance. The idea is to model spatial dependency weights as a shape constraint. There are some empirical evaluations on simulation datasets and real-world datasets. 
strengths_and_weaknesses: Strength:

* The paper solves an important problem, i.e., training explainable spatio-temporal forecasting model that can automatically learn the dependency structure.

* The paper is overall well-written and easily understandable.

Weakness:

* Although the problem of learning spatio-temporal dependency structure is interesting, the proposed solution is not well-justified. The proposed method explicitly models spatial dependency as a function of distance. But the similar philosophy has already been explored in spatial statistics, such as the Gaussian process (it represents the covariance matrix of different sample locations based on distance between those locations). 

* The proposed model seems limited in model representation with a linear function. Currently, it is not convincing that such models can achieve better performance than recent deep learning models. 
questions: 1. The Gaussian process model is geostatistics also captures the effect of weakening spatial dependency with increasing distance. How does the proposed idea compare with the Gaussian process strategy? 

2. The proposed idea is under the category of traditional machine learning methods. It is suspicious that the proposed model can outperform deep learning models in prediction accuracy. How do you explain the results in Table 1?
limitations: The paper does have some interesting discussions on the limitations of the proposed idea, e.g., not capturing the non-Euclidean space like spatial networks, and the lack of causal interpretations.
review_title: null

Meta-review: metareview: The paper proposes to use shape functions as basis functions to characterize spatial dependencies. They incorporate the shape functions into the spatial regression model and demonstrate strong forecasting performances compared to graph convolution-based methods. While the techniques are interesting, it is not directly relevant to the ICLR (deep learning) community. The argument for explainability is also subjective and less convincing.  
confidence: Certain
Decision: Reject