Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The paper presents a L0-regularized algorithm to learn sparse Hawkes-Granger models. It is well motivated from the numerical instability issue of general MLE based approach to learn MHP, and the singularity issue of existing MM-based approach that may prohibit any sparse solution. The paper is clearly presented, and empirical results from both synthetic and real datasets show competitive performance compared to other SOTA methods in learning sparse hawkes-granger models.
main_review: This paper proposes an interesting L0-regularized algorithm to learn sparse Hawkes-Granger models. It is well motivated from the numerical instability issue of general MLE based approach to learn MHP, and the singularity issue of existing MM-based approach that may prohibit any sparse solution. It has a nice analysis of why the existing L1-regularization methods may fail to recover the sparse solution. Then, it builds a connection between the Minorization-Maximization (MM) and the \epsilon-sparsity technique used for probabilistic mixture models. One additional benefit of introducing the auxiliary q_{n,i} into the optimization is that they are able to capture the instance level influence per past temporal event. Experiments on both synthetic and real datasets show that the new method is able to better recover sparse structures compared to other SOTA methods.

Limits:

The root cause of the singularity issue lies in the fact that the intensity function has to be strictly positive. The base positive background intensity for a Hawkes process still guarantees this condition when no event happens at atll. The \epsilon-sparsity technique trades off this issue by introducing the additional thresholding hyperparameter \epsilon. For the existing SOTA methods, the recovered parameters of the mutual excitation matrix can also be thresholded using a similar thresholding hyperparameter \epsilon which can be tuned using the dev dataset. I wonder how this can be compared to the proposed method. In addition, for the synthetic experiment, it will be more convincing to report the F1 metric by comparing the recovered sparsity structure to the groundtrue structure rather than showing qualitatively the sparse pattern in Figure 4. Finally, it will be more convincing to add event time prediction using MAE to evaluate the predictive performance of the new method against the baselines.

limitations_and_societal_impact: No potential negative societal impacts are involved in this paper.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This work introduces a l_0-regularized multivariate Hawkes process model for learning sparse Granger causality from temporal event data. 
On the one hand, the authors show that the prior related work cannot infer the true sparsity using l_1 or l_{1,2} regularizers. 
On the other aspect, most neural point processes for learning Granger causality, assume the equi-time-input, which prevents them from analyzing continuously observed events. 
The authors used synthetic data to compare their introduced one with neural point processes, and the counterpart model using l_1 and l_{1,2} regularizers, and demonstrate the new method can infer the true sparse impact matrix behind the events.
main_review: -Originality
To me, the new contribution by introducing l_0 regularizer, seems to be still incremental although it is the first attempt to exploit the l_0 regularizer in temporal point processes, and the other type of regularizers cannot infer the true sparse Granger causal graphs.

-Quality
The technical aspect of the paper appears to be sound. In particular, the new finding about the limitation of the l_1 and l_{1,2}-regularized Hawkes processes (HPs) in estimating true sparse impact matrices, is useful for related practitioners.

-Clarity
The paper is well written. Specifically, the limitations of the prior l_1, l_{1,2} -regularized HPs in learning true sparse Granger causal graphs, are well explained and illustrated. 

-Significance
To me, the novel l_0-regularized HP , and the proof of the limitations of the prior HPs in learning true sparse Granger causal graphs, are useful and important. Nonetheless, the aforementioned contributions seem to be still insufficient to reach acceptance level. 



limitations_and_societal_impact: -The authors do discuss some limitations of the regularized Hawkes processes in inferring Granger causal graphs from temporal event data. 
- Overall, the contribution of the paper is useful but seems to be incremental.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The authors a sparse Granger-causal learning framework for temporal event data following Hawkes process. The method utilizes the L0-regularized minorization-maximization (MM) learning framework, which remedies the issues of singularity in existing approaches.  The authors validated the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.

The contributions of this paper seem to be as follows: (1) The proposed method is the ﬁrst L0-regularized MM learning framework for the Hawkes process applied to simultaneous instance- and type-level causal analysis. (2) The proposed method can explicitly perform simultaneous instance- and type-level causal analysis.

main_review: 
There are some unclear points in this paper as described below. Although the proposed method has some novelty and the experimental results demonstrate that the performances of the proposed method were better than those of baselines in type-level tasks, due to the lack of clarity, I cannot provide higher ratings in this paper.

Specific comments:
1. L132 “When D > 1, the summation over n cannot be performed in the second term due to d_n being dependent on n. “ I cannot understand why the first term can be computed but the second term cannot be computed when D > 1 because the first term also uses d_n.
2. Theorem 1 has no proof and may be better to describe as a definition (seems to be obvious for me).  
3. L252 cLSTM and cMLP are not state-of-the-art Granger causal learning algorithms. For example, economic statistical recurrent unit (eSRU; Khanna & Tan, 2019, ICLR) and generalized VAR (Marcinkevics &  Vogt, 2020, ICLR) are more efficient and effective Granger causal learning algorithms. 
4. L268 GBR -> GPR?
5. Although the authors mentioned that “Power grid failure diagnosis” is a type-level causal diagnosis task and “data center warning event diagnosis” is an instance-level task, are the first two experiments type-level tasks? If yes, the authors demonstrate the performances of the proposed method were better than those of baselines in type-level tasks, but they are unknown in an instance-level task because there is no comparison with baselines in “data center warning event diagnosis” task. In the appendix, the authors mentioned a hard-windowing approach, but just mentioning and no numerical results. The authors introduced other approaches in the related work section, thus the comparison with baselines in an instance-level task may be required.
limitations_and_societal_impact: The limitations were mentioned. The societal impact was not mentioned but the reason was described.
review_title: null

Meta-review: The paper addresses an important problem, reviewers consider the method sound. There were some concerns that the work is too incremental I would not over estimate this issue given the relevance of the problem.

Decision: Accept (Poster)