Title: A Simple yet Scalable Granger Causal Structural Learning Approach for Topological Event Sequences
Venue: NeurIPS 2024
Accepted: yes
Keywords: Telecommunication Network Fault Diagnosis

Topological Hawkes Processes

Causal structure learning

Event Sequences

Scalability
Abstract: In modern telecommunication networks, faults manifest as alarms, generating thousands of events daily. Network operators need an efficient method to identify the root causes of these alarms to mitigate potential losses. This task is challenging due to the increasing scale of telecommunication networks and the interconnected nature of devices, where one fault can trigger a cascade of alarms across multiple devices within a topological network. Recent years have seen a growing focus on causal approaches to addressing this problem, emphasizing the importance of learning a Granger causal graph from topological event sequences. Such causal graphs delineate the relations among alarms and can significantly aid engineers in identifying and rectifying faults. However, existing methods either ignore the topological relationships among devices or suffer from relatively low scalability and efficiency, failing to deliver high-quality responses in a timely manner. To this end, this paper proposes $S^2GCSL$, a simple yet scalable Granger causal structural learning approach for topological event sequences. $S^2GCSL$ utilizes a linear kernel to model activation interactions among various event types within a topological network, and employs gradient descent to efficiently optimize the likelihood function. Notably, it can seamlessly incorporate expert knowledge as constraints within the optimization process, which enhances the interpretability of the outcomes. Extensive experimental results on both large-scale synthetic and real-world problems verify the scalability and efficacy of $S^2GCSL$.

A Simple yet Scalable Granger Causal Structural Learning Approach for Topological Event Sequences

Abstract

In modern telecommunication networks, faults manifest as alarms, generating thousands of events daily. Network operators need an efficient method to identify the root causes of these alarms to mitigate potential losses. This task is challenging due to the increasing scale of telecommunication networks and the interconnected nature of devices, where one fault can trigger a cascade of alarms across multiple devices within a topological network. Recent years have seen a growing focus on causal approaches to addressing this problem, emphasizing the importance of learning a Granger causal graph from topological event sequences. Such causal graphs delineate the relations among alarms and can significantly aid engineers in identifying and rectifying faults. However, existing methods either ignore the topological relationships among devices or suffer from relatively low scalability and efficiency, failing to deliver high-quality responses in a timely manner. To this end, this paper proposes S 2 GCSL, a simple yet scalable Granger causal structural learning approach for topological event sequences. S 2 GCSL utilizes a linear kernel to model activation interactions among various event types within a topological network, and employs gradient descent to efficiently optimize the likelihood function. Notably, it can seamlessly incorporate expert knowledge as constraints within the optimization process, which enhances the interpretability of the outcomes. Extensive experimental results on both large-scale synthetic and real-world problems verify the scalability and efficacy of S 2 GCSL.

1 Introduction

Telecommunication networks are an important component of infrastructure of modern society, where thousands of alarms may be generated by various types of faults on a daily basis. It is crucial for network operators to efficiently identify the root causes of these alarms since for every additional minute that a fault persists in telecommunication networks, it can lead to significant economic losses and cause negative public sentiment. However, the increasing scale of telecommunication networks and the interconnected nature of devices make this task particularly challenging. A single fault has the potential to trigger a cascade of alarms across multiple devices within a topological network. How to model the generation of event sequences, especially in large-scale, multi-event-type scenarios, has become more and more urgent in the telecommunication network fault diagnosis (TNFD) task.

One promising approach to understanding and predicting the generation and propagation of event sequences is the application of Granger causality analysis [Granger, 1969], which in the context of

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TNFD, can help in identifying whether a type of alarm can be the evidence of the occurrence of particular faults. As shown in the left panel of Figure 1, the mutual activation effects among various types of events are considered as a form of Granger causality and the task can be formulated as a causal structural learning problem. However, within the scope of learning Granger causality from event sequences, most of the methods rely on the assumption that event sequences are independent and identically distributed (i.i.d.). Yet, in the scenario of TNFD, the topological nature of devices inherently links events across the network, challenging the validity of such i.i.d. assumption.

Fortunately, a number of notable methods [Cai et al., 2024; Liu et al., 2024] have emerged very recently to solve the problem of Granger causal structural learning from event sequences under noni.i.d. assumptions, where the generation of alarm sequences is modeled by the topological multivariate Hawkes process (TMHP) [Cai et al., 2024]. However, all of these existing TMHP-based approaches suffer from the issue of efficiency or scalability, which is essential in the scenario of large-scale TNFD. Specifically, topological Hawkes process (THP) [Cai et al., 2024] proposes the TMHP model whose likelihood function of the Granger causal graph is optimized through a gradient-free manner, where the optimization of structure and parameter is decoupled, leading to relative inefficiency. On the other hand, the topological neural Poisson auto-regressive model (TNPAR) [Liu et al., 2024] proposes to utilize the neural point process (NPP) to implement the intensity function in TMHP, which greatly enhances the model's ability to model complex relationships among events. However, since NPP relies on deep neural networks, it lacks an analytical expression for its likelihood function. Consequently, optimization is only feasible through the prediction of event sequences, which slows down the training process and limits the model's scalability.

To address the challenges of scalability as well as efficiency presented in the TNFD task, this paper proposes S 2 GCSL, a simple yet scalable Granger causal structural learning approach for topological event sequences. S 2 GCSL utilizes a linear kernel to implement the activation effect among various event types and adopt a gradient descent manner to optimize the likelihood function. It is worth noting that multiple prior expert knowledge, namely, sparsity and acyclicity, can be integrated into this optimization procedure in a simple form of constraints, which improves the interpretability of results. Extensive experiments on both large-scale synthetic problems and a real-world TNFD problem on metropolitan telecommunication network alarm data verify the scalability and efficacy of S 2 GCSL. In a nutshell, the main contribution of this paper includes:

We propose a simple yet scalable Granger causal structural learning method, incorporating simple modeling and gradient-based optimization, to efficiently infer Granger causal graph from topological event sequences of alarms in telecommunication networks.

By incorporating experts' prior knowledge as constraints into the objective function, we provide a simple method to guarantee the interpretability during the process of optimization within the context of TNFD.

Extensive experiments show that S 2 GCSL not only achieves superior performance in effectiveness, efficiency and scalability, but also maintains robustness across diverse scenarios, validating its practical applicability in real-world telecommunication network environments.

The subsequent sections of this paper respectively recap the related work, introduce the proposed method, present the experimental results and analysis, and finally conclude the paper.

2 Related Work

Temporal Point Processes. Temporal point processes are stochastic processes used for modeling event sequences. They can be categorized into statistical point processes and neural point processes. Statistical point processes focus on developing appropriate intensity functions, often with parameters that have specific physical interpretations. Examples of statistical point processes include the Poisson process [Cox and R, 1955], Hawkes process [Hawkes and G, 1971], self-correcting process [Isham et al., 1979] and reactive point process [Ertekin et al., 2015]. On the other hand, NPP [Shchur et al., 2021] utilize the powerful learning capabilities of neural networks to implement the intensity functions, allowing the model to potentially capture complex relationships among events.

Granger Causality for Event Sequences. Various methods exist for discovering Granger causality from event sequences. For example, Hawkes process based methods [Zhou et al., 2013; Xu et al., 2016] operate on the assumption that past events stimulate the occurrence of related events in the future only if the former Granger causes the latter. However, these Hawkes process based methods significantly rely on the i.i.d. assumption, which is violated in TNFD due to the interconnected nature of devices. To address the non-i.i.d. challenge, THP [Cai et al., 2024] generalizes the Hawkes process to non-i.i.d. case by incorporating the topological information among devices. However, due to the use of gradient-free optimization to search for Granger causal structures, THP has efficiency shortcomings, which could undermine its competitiveness in the TNFD task. Inspired by THP, TNPAR [Liu et al., 2024] further proposes to utilize an NPP to model the intensity function, which significantly improves the model's capability to represent intricate event relationships. However, due to the lack of an analytical expression for the likelihood function, NPP optimization is limited to reconstructing training data from event sequences and conducting training in a supervised learning manner, which not only lacks theoretical guarantees but also performs relatively inefficient. This could make TNPAR unable to handle large-scale problems as well. Other NPP based methods include causality from attributions on sequence of events (CAUSE) [Zhang et al., 2020] and transformer Hawkes process (TransHP) [Zuo et al., 2020]. CAUSE uses an attribution method to extract Granger causality from the well-trained NPP, and in TransHP, the temporal dependencies among event sequences are captured by a transformer. These NPP based methods are typically flexible, and thus can incorporate topology information through some modifications. Unfortunately, the scalability of these methods are also not ideal due to the same reason as TNPAR.

In a different context, our work is also related to Granger causal discovery from time series. In [Brillinger and R, 1994], researchers aggregate event sequences into time series, enabling the analysis of event sequences using auto-regressive models. Amortized causal discovery (ACD) [Löwe et al., 2022] applies an amortized model to infer Granger causal structures from time series. In addition, PC with momentary conditional independence test (PCMCI) [Runge, 2020] and methods based on transfer entropy [Mijatovic et al., 2021; Chen et al., 2020], are founded on strict causal assumptions rather than Granger causality and utilize independence tests or measures to discover the causal structure from event sequences.

3 The Proposed S 2 GCSL

3.1 Problem Formulation

In the problem of learning Granger causal structure from topological event sequences in telecommunication networks, suppose the topological connections between devices are represented as an undirected graph G N ( N , E N ) , where N is the device set and the edges E N indicate physical connections between these devices. Besides, a directed graph G V ( V , E V ) captures the Granger causal relationships among different event types V , with E V representing the causal edges between two different event types. In this scenario, an event can not only influence future events at its location but also at devices that are topologically connected to it.

Given this setup, we consider topological event sequences of length m , denoted by X = { ( v i , n i , t i , ℓ i ) | i ∈ { 1 , . . . , m }} . These sequences arise from the causal interactions defined in

G V and occur within the structure of G N . Here, v i ∈ V represents the event type, n i ∈ N denotes the device where the event occurs, t i ∈ [0 , T ] refer to the start timestamps of the event and ℓ i ∈ Z + denotes how many timestamps the event last. We can model the occurrence of these events as a series of counting processes { C v,n ( t ) | v ∈ V , n ∈ N , t ∈ [0 , T ] } , where C v,n ( t ) counts the number of times event type v has occurred at device n up to time t . For practical analysis, the continuous interval [0 , T ] is segmented into ⌈ T/ ∆ ⌉ smaller intervals, where ∆ ∈ R + is chosen based on the application context. The number of occurrences within these intervals are recorded as O V , N = { O v,n t | t ∈ { 1 , . . . , ⌈ T/ ∆ ⌉} , v ∈ V , n ∈ N } , where O v,n t = C v,n ( t × ∆) -C v,n (( t -1) × ∆) reflects the occurrences of event type v on device n within the interval (( t -1) × ∆ , t × ∆] .

Assuming that the counting processes within each time interval follow a Poisson process, where the intensity λ v,n t refers to the expected number of occurrences in an interval of event type v on device n at time t , and the probability of observing O v,n t occurrences can be formulated using the Poisson probability function as follows:

This sets the stage to define the problem of causal discovery from topological event sequences as Definition 1 below.

Definition 1 (Granger Causal Discovery from Topological Event Sequences) . Given the records of event sequences X = { ( v i , n i , t i , ℓ i ) | i ∈ { 1 , . . . , m }} , and the existing topological network G N ( N , E N ) , the objective of Granger causal discovery from topological event sequences is to deduce the Granger causal graph G V ( V , E V ) among the event types.

To address this problem, we introduce the S 2 GCSL model, which includes both a generation process and an inference process.

3.2 Generation Process of the Event Sequences

The generation process of S 2 GCSL is illustrated with solid lines in the right panel of Figure 1 , where the occurrence O v i ,n j t is influenced by historical event sequences X h = { ( v i , n i , t i , ℓ i ) | t i < t ≤ t i + ℓ i } , along with two types of matrices, A and B 0: k . Here, A is a | V | × | V | binary matrix indicating Granger causality between event types. The element A v i ,v j from matrix A at row i and column j denotes the causality: if A v i ,v j = 0 , it means that there is no Granger causality between event type v i and v j . Otherwise, there exists a causality. B 0: k represents a set of matrices { B 0 , B 1 , . . . , B k } , where each B k is a | N | × | N | binary matrix showing the physical connections between devices at a geodesic distance [Bouttier et al., 2003] of k within G N . The element B k n i ,n j in matrix B k at row i and column j specifies this connection: if B k n i ,n j = 1 , then the geodesic distance between device n i and n j is less than or equal to k . Otherwise, B k n i ,n j is set to 0 .

In this paper, we utilize a linear activation function to model the causal relationships among event types, and the intensity λ v,n t of an event type v on a device n is given as:

where µ v,n is a constant representing the baseline intensity of event type v on device n and α v i v is a coefficient denoting the activation intensity of event type v i on event type v , which can be considered as the Granger causality of v i → v . ∑ i : t i <t ≤ t i + ℓ i means the summation over all the events j that the event i occurs during the duration of j .

Counterintuitively, such a simple assumption based on linear activation function can effectively model complex functions that depict how event intensities vary over time. This capability arises because the intensity of an event at a given time may be influenced by countless preceding events. Even though the impact of each individual event is simple, the superposition of numerous linear functions can approximate arbitrarily complex intensity functions.

3.3 Inference Process of the Granger Causal Graph

The inference mechanism of S 2 GCSL is illustrated with dashed lines in the right panel of Figure 1. The diagram indicates that the causal matrices A are deduced by integrating the current event occurrences X ( t 0 ) , historical event sequences X h = { ( v i , n i , t i , ℓ i ) | t i < t ≤ t i + ℓ i } , and the topological network B 0: k .

Considering the generation model defined in Eq. 2, the coefficient α v i v is treated as the Granger causality statistic of event type v i on event type v . Consequently, the weighted Granger causal matrix A ′ ∈ R | V |×| V | , where A ′ i,j = α i,j × A i,j , along with the baseline intensity matrix µ can be seen as the parameters of the generation model Θ = { A ′ , µ } , and the log-likelihood function of Θ given the observed event sequences X = { ( v i , n i , t i , ℓ i ) | i ∈ { 1 , . . . , m }} can be expressed as follows:

where ∑ i : n i = n means the summation over all the events i that occur on device n . With such loglikelihood function, the Granger causal discovery problem can be transformed into the following optimization problem that estimates the optimal parameters Θ ⋆ = { A ⋆ , µ ⋆ } as:

where A ⋆ denotes the inferred weighted Granger causal matrix.

As mentioned before, some prior expert knowledge of the causal structures in the TNFD scenario should be taken into consideration to ensure the inferred causal graph interpretable. Specifically, we focus on two properties of the causal graph among event types, namely sparsity and acyclicity. The sparsity of activation effects suggest that most event types only influence a small fraction of other event types in telecommunication networks. The sparsity can be reflected in the entry-norm constraint of A ′ as:

where || A ′ || 1 denotes the 1 , 1 entry-norm of A ′ and ϵ is a small positive constant.

Besides, acyclicity suggests that the activation effects among event types should not form cycles and there is no self-excitation. As a result, the deduced causal graph should a DAG, which motivates us to introduce the acyclic constraint [Zheng et al., 2018] as:

where I is the identity matrix, β is a constant and ◦ denotes the Hardamard product. Consequently, the optimization with constraints can be written as:

By leveraging the Lagrangian multiplier method, the final optimization problem is defined as:

where λ 1 and λ 2 refer to the regularized hyperparameters. For the optimization procedure, the Adam optimizer [Kingma and Ba, 2015] which is known for its efficiency and stability is adopted with learning rate lr = 0 . 05 .

After the optimization, we got the weighted Granger causal matrix A ⋆ , and to deduce the final binary adjancency matrix A , edges with too small weights are pruned, i.e.,

and ρ is a constant hyperparameter to control the pruning threshold.

4 Experiments

In this section, we will implement the proposed S 2 GCSL method and the baseline approaches on both simulated data and metropolitan telecommunication network alarm data. All methods will undergo testing using 10 different random seeds, and the results will be reported in the form of mean and standard deviation over these 10 repetitions. The evaluation metrics for the experiments will encompass F1 score [Powers, 2020], Structural Hamming Distance (SHD), and Structural Intervention Distance (SID) [Peters and Bühlmann, 2015].

Specifically, precision denotes the proportion of predicted edges that are actually present among the true edges, while recall represents the proportion of true edges that have been correctly predicted. F1 score is the weighted harmonic mean of both Precision and Recall, and is calculated as F 1 = 2 × Precision × Recall Precision + Recall , the higher F1 score the better ( ↑ ). SHD indicates the number of edge insertions, deletions, or flips required to transform one graph into another, the lower SHD the better ( ↓ ). SID is a measure that quantifies the similarity between two DAGs based on their corresponding causal inference statements, the lower SID the better ( ↓ ).

In experiments, we use the following Granger causal discovery methods as comparisons: TNPAR [Liu et al., 2024], ADM4 [Zhou et al., 2013], CAUSE [Zhang et al., 2020], PCMCI [Runge, 2020], MLE_SGL [Xu et al., 2016] and ACD [Löwe et al., 2022]. We would like to point out that THP [Cai et al., 2024] and TransHP [Zuo et al., 2020] are not included because they are too inefficient to produce results within required time under most settings. All the experiments are conducted on a Linux server with two 3.00GHz Intel Xeon Gold 6354 CPUs and one RTX3090 GPU. All the models are implemented by PyTorch [Paszke et al., 2019], and the code is available at https: //github.com/MingjiaLi666/S2GCSL .

4.1 Implementation and Hyperparameters

In the algorithm implementation of S 2 GCSL, the involved hyperparameters include: the geodesic distance in the topological network k , the regularization coefficients λ 1 , λ 2 and the pruning threshold ρ . In the synthetic experiments, we set these hyperparameters as follows: k = 2 , ρ = 1 × 10 -3 . Worth noting that the proper values of λ 1 and λ 2 are related to the scale of sample size and thus vary over different settings. We adopt a heuristic way to estimate the proper range of λ 1 , λ 2 that calculate the local gradient of loss over || A ′ || 1 and h ( A ′ ) respectively. In the real-world experiments, we set the hyperparameters as follows: k = 1 , ρ = 5 × 10 -4 , λ 1 = 5 × 10 5 and λ 2 = 1 × 10 5 .

4.2 Synthetic Experiments

4.2.1 Synthetic Experimental Setup

The synthetic data is generated in the following manner: a) A Granger causal graph and a topological graph are randomly created using Erd ¨ os R ´ enyi random graph generator. b) Root event records are produced using a Poisson process with a base intensity parameter µ in the Hawkes process. These root event records occur spontaneously within the system. c) Based on the root event records, propagated event records are discretely generated according to both the time interval ∆ and the excitation coefficient α . It is worth noting that event sequences can be sparse in real-world scenarios. To address this, a time interval parameter ∆ is introduced to the generation process, dividing the time domain [0 , T ] into small intervals with indexes as { 1 , . . . , ⌈ T/ ∆ ⌉} where ⌈·⌉ refers to the ceiling function. Then, the event records can be summarized within the same timestamp. Note that ∆ ≥ 0 , and ∆ = 0 implies the use of the original event sequences. The simulated data is generated by systematically varying one parameter at a time in the generation process, while keeping the default parameters constant. The parameters included in the generation

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process are as follows: the number of devices ( | N | ), the number of event types ( | V | ), the sample size ( m ), the range of baseline intensity ( µ range), the range of activation intensity ( α range) and the time interval ∆ . The ranges of the above parameters are: | N | = { 20 , 40 , 60 , 80 } , | V | = { 5 , 10 , 15 , 20 , 25 , 50 , 100 } , m = { 50 000 , 100 000 , 150 000 , 200000 , 250 000 , 300 000 } , µ range ( × 10 -5 ) = { (1 , 3) , (3 , 5) , (5 , 7) , (7 , 9) } , α range ( × 10 -2 ) = { (1 , 2) , (2 , 3) , (3 , 4) , (4 , 5) , (5 , 6) } and ∆ = { 1 , 2 , 3 , 4 , 5 } , where the default parameters are denoted in bold.

4.2.2 Results on Synthetic Data

Effectiveness. The F1 Score, SHD and SID of different methods on the synthetic data are shown in Figure 2, 3 and 4 respectively. Note that if the result for a particular baseline is missing at some points, it indicates that the method is unable to produce results within 1 hour (S 2 GCSL gives results for problems with 100 event types in approximately 9 minutes.) under the setting of such points. Based on the results depicted in these 3 figures, S 2 GCSL exhibit superior effectiveness across all scenarios when compared to other baselines. Besides, from Figure 2, S 2 GCSL demonstrates strong robustness across all parameters including both baseline activation intensity, the sample size of data, the time interval of recording, the causal graph scale and the topological network scale. Such results indicate the robustness of S 2 GCSL, i.e., S 2 GCSL is expected to be effective in most scenarios.

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Efficiency. The wall-clock execution time results of different methods on different scale of problems are presented in Table 1. According to Table 1, S 2 GCSL is able to produce results within 10 minutes even for problems scaling up to 100 event types. Worth noting that only two of the compared methods, namely S 2 GCSL and ADM4, are scalable to problems with 50 event types, both of which have nearly an order of magnitude advantage on efficiency over other methods in comparison. Besides, compared to ADM4, S 2 GCSL is more efficient on larger-scale problems (25 and 50), indicating its greater potential for application in large-scale real-world scenarios (Given that the real-world problem involved in this paper is with 38 event types).

Summary. To sum up, considering both effectiveness and efficiency, S 2 GCSL demonstrates clear advantages in effectiveness and scalability compared to other methods, thanks to its simple yet problem-adapted design. In the next subsection, this paper will study the performance of S 2 GCSL on a real-world TNFD task in metropolitan telecommunication networks.

4.3 Real-World Experiments

4.3.1 Metropolitan Telecommunication Network Alarm Data

The real-world dataset utilized in this study was sourced from a business setting in metropolitan telecommunication network collected by a multinational communications company and is accessible through the NeurIPS 2023 competition of Causal Structure Learning from Event Sequences and Prior Knowledge 3 (Phase 2 real-world dataset). It comprises a sequence of alarm records generated based on both a topological network G N and a causal structure G V . The topological network G N consists of

65 devices, and the alarm records cover 38 types of alarm events, amounting to 492,877 alarm event records. It is worth noting that, due to the equipment characteristics and as verified by experts, the collected timestamps of alarm events display specific time intervals.

4.3.2 Results on Metropolitan Telecommunication Network Alarm Data

The results of the experiments on metropolitan telecommunication network alarm data can be found in Table 2, where the F1 Score, SHD, SID and wall clock execution time (ET(s)) for the compared methods are reported. The results show that the methods incorporating the topological network (S 2 GCSL, CAUSE and TNPAR) outperform those that rely on the i.i.d. assumption with respect to F1 Score. This suggests that in the real-world telecommunications networks, alarm events do indeed propagate through devices within the topological network, consistent with the expert's knowledge and our model assumptions. However, both TNPAR and CAUSE take over an hour (for CAUSE, it needs 2 hours) to produce results, which is unacceptable in the race against time for TNFD, compared to just over ten minutes for S 2 GCSL. From the perspective of effectiveness, S 2 GCSL shows the highest F1 Score and the lowest SHD, indicating its relative insensitivity to weak Granger causal strength between event types, which may exhibit in real-world scenarios [Liu et al., 2024]. Additionally, S 2 GCSL achieves a good SID, only being slightly higher than PCMCI (however, this is because PCMCI often deduce very sparse causal graphs), which highlight S 2 GCSL's superior capability for causal inference [Peters and Bühlmann, 2015]. Therefore, from a comprehensive perspective, only S 2 GCSL has the potential to be applied and work well in real-world scenarios.

5 Conclusion

This paper addresses the critical issue of fault diagnosis in large-scale telecommunication networks by proposing a simple method for efficient and scalable Granger causal structural learning from topological event sequences. The proposed approach, referred to as S 2 GCSL, leverages a linear kernel to model the activation effects among different event types and uses gradient descent for the optimization of the likelihood function. This method simplifies the modeling and the optimization process to enhance the scalability and efficiency of inferring causal structures from large datasets of network alarms. Besides, S 2 GCSL also include the integration of expert knowledge as constraints within the optimization process, ensuring the model's explainability via aligning with domain-specific insights, which is crucial for practical applications. By conducting extensive experiments on both synthetic datasets and real-world data from a metropolitan telecommunication network, we verify that S 2 GCSL significantly outperforms existing methods in terms of scalability or efficiency, while maintaining good effectiveness.

Despite the advancements presented in this paper, there are several limitations that suggest avenues for future research. Firstly, while S 2 GCSL provides an efficient solution for large-scale datasets, its application is currently limited by the simplicity of its modeling approach. The linear kernel may not capture the full complexity of interactions in more dynamically evolving network environments where non-linear relationships and non-stationary patterns prevail. Additionally, further research could focus on extending the applicability of S 2 GCSL to other types of networks, such as power grids

or transport networks, where similar challenges in fault diagnosis are present. This would involve adapting the current framework to different kinds of event data and potentially different topologies.

Acknowledgments

The authors would like to express the sincere thanks to the anonymous reviewers for their constructive and helpful comments. This work is supported by the National Natural Science Foundation of China (62476091, 62106076).

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents S2GCSL (Simple yet Scalable Granger Causal Structural Learning), a novel method for learning Granger causal graphs from topological event sequences in telecommunication networks. The authors present a simple and scalable method that uses a linear kernel to model activation interactions between event types, and employ gradient descent to efficiently optimize the likelihood function. The method has the ability to incorporate expert knowledge as constraints during optimization, and is with high interpretability. This paper addresses the limitations of existing methods that either ignore topological relationships between devices or lack scalability. The effectiveness, efficiency, and scalability are verified by experiments on both synthetic and real-world telecommunication network fault diagnosis problems. The method can learn causal structures from large-scale alarm data, help identifying root causes of faults in complex telecommunication networks.\n\nSTRENGTHS:\nThe authors present a novel method for Granger causal structural learning tailored specifically for TNFD. The novelty is manifested through innovative problem formulation that incorporates topological event sequences and integrates expert knowledge as constraints to enhance interpretability. \n\nThe method combining linear kernels with gradient descent optimization is solid. The experiments are sensible and supportive. The writing is overall good.\n\nThe most surprising thing to me is, this paper offers a scalable and efficient solution to a important real-world problem, with potential applications extending beyond telecommunications to other complex networked systems. I am excited to see that a causal learning method can be properly used in a practical scenario.\n\nWEAKNESSES:\nThe S2GCSL is implemented on batch data. In practical telecommunication network, it is possibly required that fault diagnosis and causal learning are implemented in a real-time fashion. It will be better if the authors can discuss the ability of the proposed method to enable real-time processing and decision-making. For instance, consider an online learning setting instead that continuously updates the causal model as new data arrives could significantly enhance its practical ability.\n\nBesides, in real-world problems, it is possible that there are some missing entries or noise. I suggest the authors discuss how S2GCSL can handle such cases. \n\n\ntypos:\nAbstract: \"Recent years have seen a growing focus on a causal approach to...\" -> \"Recent years have seen a growing focus on causal approaches to\"\n\nLine 47: \"...relatively inefficiency\" -> \"...relative inefficiency\"\n\nQUESTIONS:\n1. As pointed by Weakness 1 and Weakness 2, how can S2GCSL be used in practical online setting where data arrives continuously?\n\n2. The authors claim that they could learn Granger causality efficiently on large-scale problems. Could the authors provide some clues about the scale range of problems in real-world scenarios? There are 38 nodes in the real-world dataset used in the experiments.\n\nLIMITATIONS:\nNo.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents S2GCSL, a novel method designed to efficiently identify the root causes of alarms in telecommunication networks by learning Granger causal graphs from topological event sequences. This method uses a linear kernel and gradient descent optimization, while incorporating expert knowledge as constraints to enhance interpretability. Extensive experiments on both synthetic and real-world datasets demonstrate that S2GCSL is highly scalable and effective, outperforming existing methods in terms of efficiency and robustness. The primary contributions include the introduction of a scalable causal learning approach, the integration of expert knowledge, and comprehensive validation of the method's applicability in real-world scenarios.\n\nSTRENGTHS:\nThis paper demonstrates strengths across multiple dimensions. Its originality lies in the novel formulation of Granger causal discovery for non-i.i.d. topological event sequences, the creative combination of a linear kernel with gradient-based optimization, and the innovative integration of expert knowledge as constraints. \n\nThe quality is evident in its solid theoretical foundation, comprehensive experimentation on both synthetic and real-world data, and thorough comparative analysis against state-of-the-art methods. \n\nThe paper's clarity shines through its well-structured presentation, clear problem definition, step-by-step methodology explanation, and effective use of visual aids. \n\nThe significance of the work is substantial, addressing critical scalability issues in analyzing large-scale telecommunication networks, offering practical applicability through the incorporation of domain knowledge, and potentially impacting broader fields involving topological event sequences. \n\nBy bridging the gap between theoretical Granger causality analysis and practical fault diagnosis in complex networks, S2GCSL represents a noteworthy advancement in the field, with implications for both research and real-world applications in network analysis and fault diagnosis.\n\nWEAKNESSES:\nThe performance of the S2GCSL method relies on several hyperparameters, such as the geodesic distance k, regularization coefficients \\lambda_1 and \\lambda_2, and the pruning threshold \\rho. The paper should provide more detailed guidelines or heuristics for tuning these hyperparameters in various network settings. \n\nWhile integrating expert knowledge as constraints is a strength, the paper does not thoroughly discuss the potential impacts of incomplete or inaccurate expert knowledge. For example, dense causal graph.\n\nThe writing should be improved, some minor issues:\nImprove transitions between sections for better flow. For instance, adding a brief summary at the end of the \"Related Work\" section could help readers transition more smoothly to the \"Proposed Method\" section.\n\nEnsure all references are formatted according to the same style guide. For instance, \"[Granger and CWJ, 2001]\" seems a little wired.\n\nKeep consistent with the use of Fig., Figure, Table through the paper. For example, use abbreviation Fig. In the text but Table not abbreviated, and Figure in the caption. \nQuestions\n\nQUESTIONS:\n1. The choice of hyperparameters like the geodesic distance k, regularization coefficients \\lambda_1 and \\lambda_2, and the pruning threshold \\rho are crucial for the performance of the method. I assume you have some techniques for adjusting these parameters, could you briefly explain them?\n\n2. The paper integrates several expert knowledges into the optimization process. However, if the expert knowledge is not the case, e.g., for the sparsity constraints, what is the graph density applied in the synthetic experiments? What if the actual graph is not sparse, how to modify S2GCSL to adapt the situation? \n\n\n3. I notice a phenomenon: In Table 1, as the problem scale increases, the efficiency of ADM4 gradually surpassed that of S2GCSL, but it fell behind again for the largest 50 and 100 node problems. Have you analyzed why this might be the case?\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper presents S2GCSL, a scalable and efficient method for Granger causal structural learning from topological event sequences, specifically designed for telecommunication network fault diagnosis. The approach uses a linear kernel to model interactions and employs gradient descent for optimization, incorporating expert knowledge as constraints to enhance interpretability. Extensive experiments on synthetic and real-world datasets demonstrate the method's superior performance in scalability and efficacy compared to existing methods.\n\nSTRENGTHS:\nThe paper demonstrates substantial strengths across multiple dimensions: originality, quality, clarity, and significance. \n\nIt introduces an original approach, S2GCSL, for Granger causal structural learning tailored for TNFD, effectively addressing the unique challenges posed by topological event sequences. This originality stems from the novel problem formulation that integrates topological relationships and expert knowledge into the causal learning process, distinguishing it from traditional i.i.d. assumptions. \n\nThe quality of the work is underscored by rigorous methodology and extensive experiments, which validate the scalability and efficiency of the proposed method on both synthetic and real-world datasets. \n\nThe clarity of the paper is commendable, with well-organized sections and easy-to-follow explanations of complex concepts, although there is some room for improvement in detailing certain methodological aspects and transitions between sections.\n\nThe significance of the research is substantial, offering a robust and interpretable solution to a critical real-world problem, with potential applications beyond telecommunications to other complex networked systems such as power grids and transportation networks. By addressing the limitations of existing methods, the paper makes a noteworthy contribution to the field of causal inference and network fault diagnosis.\n\nWEAKNESSES:\nSome of the assumptions in the paper may be a little bit strong. Firstly, the paper assumes that the counting processes within each time interval follow a Poisson process. This assumption may not hold in all real-world scenarios, especially in cases with over-dispersed data or memory effects. The authors should explore the robustness of their method to violations of this assumption and consider discussing potential adaptations or extensions that can handle more general or alternative event processes, such as over-dispersed Poisson or negative binomial distributions.\n\nSecondly, the S2GCSL method currently assumes stationarity in the causal relationships. In real-world networks, causal relationships may change over time. The authors should address this limitation by proposing potential extensions or methodologies for adapting the model to dynamic environments. For instance, incorporating online learning techniques or adaptive methods that can update the causal structure as new data arrives could significantly enhance the practical utility of the approach.\n\nBesides, comparing the results on synthetic data and metropolitan telecommunication network alarm data, it shows that S2GCSL suffers a performance drop when transitioning from synthetic to real-world cases. It would be beneficial for the authors to provide a more detailed analysis of this phenomenon.\n\nQUESTIONS:\n1. The paper assumes that the counting processes within each time interval follow a Poisson process. How would the S2GCSL method perform if the underlying data generation process deviates from the Poisson assumption, for example, if the data exhibit over-dispersion or if the event occurrences are not memoryless?\n\n2. The proposed method assumes a stationary environment for modeling the Granger causality. How does the S2GCSL approach handle non-stationarity in the event sequences, where the underlying causal relationships might change over time? Are there mechanisms in place to adapt to such changes dynamically?\n\n3. The synthetic data is generated under specific assumptions. How well do these synthetic datasets represent real-world cases? What gaps still exist between the synthetic data generation process and real-world scenarios?\n\nLIMITATIONS:\nNone", "TITLE": "Official Review", "RECOMMENDATION": 8, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents S2GCSL, a novel approach for Granger causal structural learning from topological event sequences in telecommunication networks. The methodology leverages a linear kernel to model interactions among event types and employs gradient descent for efficient optimization of the likelihood function. Unlike existing methods, S2GCSL integrates expert knowledge as constraints, enhancing the interpretability of results. Extensive experiments on both synthetic and real-world datasets demonstrate the approach's scalability and efficacy, addressing the challenges of fault diagnosis in large-scale, interconnected network environments.\n\nSTRENGTHS:\n- The paper presents a highly original approach to telecommunication network fault diagnosis (TNFD) through the development of S2GCSL, a scalable Granger causal structural learning method tailored for topological event sequences.\n- The originality is evident in the innovative problem formulation that leverages the unique structure of telecommunication networks, integrating expert knowledge constraints to enhance interpretability and address existing limitations in the field. \n- The quality of the research is underscored by a rigorous methodology, employing linear kernels and gradient descent optimization, and validated through extensive experiments on both synthetic and real-world datasets. \n- Clarity is maintained throughout the paper, with well-organized sections and clear explanations of complex concepts, making the work accessible to a broad audience. \n- The significance of this work is substantial, offering a robust and efficient solution to a critical problem in telecommunication networks, with potential applications extending to other domains such as power grids and transport networks. By addressing scalability and interpretability issues, the paper makes a notable contribution to the fields of causal inference and network fault diagnosis.\n\nWEAKNESSES:\n- The method is primarily tested on telecommunication networks. It would be helpful for the authors to discuss the scalability and applicability of the S2GCSL method to other types of network topologies, such as hierarchical, mesh, or dynamically evolving networks. Providing theoretical insights or preliminary experimental results on these different network structures would strengthen the argument for the method’s generalizability.\n- It would be better for the paper to discuss how the S2GCSL method can be adapted for online cases where data arrives continuously and decisions need to be made online. This limitation raises concerns about the method's applicability in scenarios requiring immediate fault diagnosis and response in telecommunication networks.\n- The paper specifies the computational resources used for the experiments; however, it does not address how the S2GCSL method would perform on less powerful hardware, since in practical deployment, there may be a need for each signal source to perform fault diagnosis online independently, and the computational resources of these signal sources are often limited. This raises concerns about the feasibility of deploying the method in resource-constrained environments, which may limit its practical applicability.\n\nQUESTIONS:\n- The method is tested on a specific telecommunication network topology. How well does the S2GCSL method scale to different network topologies, such as hierarchical or mesh networks? Have there been any tests or validations on networks with varying levels of connectivity and complexity?\n- The paper uses a linear kernel to model activation interactions among event types. Have other types of kernels been considered or tested, such as polynomial or exponential kernels? What led to the decision to use a linear kernel specifically?\n- The synthetic data is generated using specific parameters and distributions. Have other synthetic data generation techniques been considered?\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2024-07-12"}