Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: the paper proposes a more general form of kernel function that is typically used in temporal/spatio-temporal point process, by considering an absolute time-dependent component in addition to the relative spatial-time inputs. In addition, authors made another contribution by proposing a more efficient approach  to ensure the positivity of intensity in the form log-barrier to the optimization problem. Empirical results show both accuracy and efficiency gain over baselines. 
strength_and_weaknesses: Strength:
a new kernel method is proposed by considering absolute time
complexity analysis is provided
empirical evaluation performance is strong

Weakness:
additional empirical study would provide more understanding of the method. 

Other comments:
- A baseline RNN model with the s and t as an input to RNN, which models time-dependent change in function and similar to your base kernel, should be considered. It would highlight the necessity of using kernel. 
- Background does the spatial aspect of the STPP indicate that the change in location always be positive in location? what's an example for such application?
- does the grid resolution have impact on the learning of the kernel?
- would a large t value, corresponding to long term dependency, pose any numerical issue ? 
- Eq4: it would be helpful if there is some formal statement on assumptions, the generalization result or its expressivity related to Eq 3.  
- Table 3: how does DNSK+softplus compare with transformer results? Would using barrier improve THP as well?

clarity,_quality,_novelty_and_reproducibility: quality: good

clarity: good

originality: good
summary_of_the_review: novel formulation on the new kernel with promising results.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper proposes a deep non-stationary kernel for spatio-temporal point processes using a different parameterization scheme, which reduces the model complexity. The non-negativity of the solution is guaranteed by a log-barrier method which maintains the linearity of the conditional intensity function. In addition, a computationally efficient strategy for model estimation is introduced. Both the synthetic and real data sets are used to validate the superiority of the proposed model. 
strength_and_weaknesses: Strength:
1. The proposed methods significantly reduces the model complexity without sacrificing the performances. The motivation is clear and the contribution is satisfied.
2. Comprehensive and well designed experiments are conducted.
3. This paper is easy to follow with good presentation.

Weaknesses:
1. Some preliminary knowledge needs to be included to make the paper self-contained. For example, it would be better to briefly describe the "mask point process".
2. Some notations need more clarifications. For example, what "B" refers to in Equation 2. And what the dimension of "s". In Equation 4, there is operation of "s-s'", while "s" refers to the location which should be a 2-D or 3-D value. How the "-" operation is conducted in these values?
3. More discussions on the motivation of specific techniques can be provided. For example, compared to directly using the neural network, what is the advantage of the kernel in Equation 4. 
4. No clear problem formulation. For better understanding the problem and methodology, it will be great to have a formal problem formulation. 
5. The meaning of "testing l" in Table 4 is not explained. 

clarity,_quality,_novelty_and_reproducibility: 1. This paper have a clear presentation towards the methodology. The authors does not provide the source codes and there are no detailed hyper-parameters towards the architecture of the model.
2. The novelty of this paper is satisfied, which proposes a deep non-stationary kernel for spatio-temporal point processes using a different parameterization scheme. Additional optimization strategy is accommodated with the proposed schema.
summary_of_the_review: The major contribution of this paper is to largely reduce the complexity of the existing neural kernel-based approach towards the spatial-temporal point process. The proposed technique is novel and technical sounds. Though no much improvement on performance and the paper is not solving a new problem, the complexity is largely reduced without sacrificing the performance. Thus, I admit the  contribution and novelty of this paper are above-average. There are some minor issue towards statements and descriptions which have been mentioned above.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This manuscript proposes a method to model non-stationary spatio-temporal events in the framework of hawkes process. The specific method is to construct a more refined kernel function.
strength_and_weaknesses: Strength:
1. The idea of using deep non-stationary kernel in the point process to model spatial-temporal data is interesting and somewhat novel.
2. The method is clear and computational complexity is made.
3. The experiments are sufficient to demonstrate the effectiveness of the proposed method.



Weaknesses

1. The kernel k is designed with heuristics, and can it guarantee that k has good properties, such as to be positive definite?
2. It is said that " (ii) The non-stationarity of events’ influence over spatial-temporal space can be conveniently captured by non-constant psi_l and u_r". I wonder if this is like a kind of positional coding of time index? If so, transformer also has the ability to model non-stationary temporal data, and the experimental results show that THP performs comparable as the proposed methods. The authors did not make a detailed analysis of THP, nor did they compare the differences and advantages of THP with the proposed methods.
clarity,_quality,_novelty_and_reproducibility: This manuscript is clear and somewhat novel.
summary_of_the_review: It is an interesting work on modeling non-stationary spatial-temporal data and the proposed method is solid and demonstrated to be effective.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The authors of this submission proposed a deep non-stationary kernel (DNSK) modeling Spatio-Temporal Point Processes (STPP) for potentially non-stationary events in continuous time and space. 

The authors focused on Hawkes process assuming that the influences from the past events are linearly additive and in turn modeled the conditional intensity function as $\lambda(t, s) = \mu + \sum_{History} k(t, t', s, s')$, where $k(t, t', s, s')$ is named as the influence kernel function, which captures the spatio-temporal dependency. Specifically, DNSK assumes a factorized kernel along time and space directions, as well as potential event "marks" when they are available to handle potential computational challenges. Furthermore, by considering parametrization with "displacement", the authors claimed that DNSK achieves low-rank kernels for more efficiency. The log-barrier method is introduced to preserve non-negativity of the conditional intensity function, also maintaining model interpretability and computational efficiency. 

Experiments were performed comparing some existing methods: RMTPP, Neural Hawkes (NH), Transformer Hawkes process (THP), Parametric Hawkes process (PHP), Neural spectral marked point processes (NSMPP) with the proposed DNSK without log-barrier but with a non-negative softplus activation function (DNSK+Softplus). The results showed that the proposed method can indeed capture the non-stationarity and achieve good model recovery and event prediction performances.  
strength_and_weaknesses: Efficient modeling non-stationary spatio-temporal processes is challenging. The authors followed recent efforts, in particular Zhu et al. 2022, Zou et al. 2020, etc. to develop a "displacement"-parametrized neural network based kernels in a Hawkes process model to address the potential computational challenges. The empirical results demonstrated the efficacy of their proposed DNSK. 

Clearer discussion besides the illustration in Figure 1 may be needed for clearer motivation and insights. For example, it may be necessary to discuss the pros and cons of factorized kernel assumptions and displacement-based parametrization. When introducing Figure 1, the authors may want to briefly mention the computational advantages and difference of the actual event prediction performance before and after using "displacement" on the kernels with the same rank. Although the figure did show that the displacement-based kernel matrix with rank 7 also has three peaks as the original kernel with rank 298, it may be necessary to provide numerical kernel performance measure. The authors may also want to discuss more about the reason for building up the kernels using linear combinations of MLP-based basis functions. As MLPs are assumed to have good approximation capability, is it still necessary to have the linear combination of these MLPs to make the kernel more complicated? 

The authors may want to make there empirical performance comparison results more consistent to have all the results reported from all the selected baselines. For example, it may be interesting to explore on the effectiveness of log-likelihood because the potential mismatch of log-likelihood and MSE regarding the THP performance on 1D Data set 2 and 1D Data set 3. For the real-world data, instead of showing the performances of some baselines, the authors may want to present the results from all the applicable baselines. 




clarity,_quality,_novelty_and_reproducibility: DNSK appears as an extension of previous neural process models with "displacement"-based factorized neural kernels. Such an implementation does provide some performance improvement based on the reported experiments. 

Overall presentation is reasonable clear. The authors may want to consider further improve the presentation, for example, better justify the adopted kernels. There are also several language problems throughout the submission: for example. $B(s,\Delta s)$ seems to be a ball set with the center $s$ and radius $\Delta s$ but is not defined; symbol $f$ is used as transformation in page 3 but as pdf of the event in page 8;  and many others throughout the submission. 
summary_of_the_review: The authors proposed DNSK to efficiently model potentially non-stationary events in continuous time and space. Empirical performance comparison results have shown the efficacy of the proposed DNSK methods. Better justification of the adopted kernels, in particular linear combination of MLP-based kernel bases, may be needed. More comprehensive empirical experimental results may need to be provided to confirm the benefits of DNSK compared to the previous similar efforts. 

====post-rebuttal====

I truly appreciate the extensive efforts from the authors to address my questions.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: This paper adds to the burgeoning literature on spatiotemporal point process modeling by introducing a new non-stationary influence kernel. Computational efficiency is achieved through a low-rank representation. The reviewers found the presentation clear and well-motivated, and complimented the experiments. There were a number of suggestions made by the reviewers, all of which are very do-able, and I expect the authors to follow them in revising the paper.
justification_for_why_not_higher_score: Perhaps it should be higher--I'm not totally convinced though.
justification_for_why_not_lower_score: Authors were in agreement.
Decision: Accept: poster