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Resilient Concurrent Causal Discovery for Topological Event Sequences

Jiyu Tian, Junhao Dong, Mingchu Li, Lingling Fang, Liming Chen, Andreas Holzinger, Zheng Yan, Yew Soon Ong

arXiv:2608.21815v1cs.LG

TL;DR

Existing causal-discovery methods struggle with concurrent causal relationships and incomplete event sequences in telecommunication networks. RCCD combines influence-aware hyperedge causal attention with mask-based alternating optimization, and experiments on synthetic and real-world datasets report improved accuracy and robustness over existing methods.

  • Problem

    Existing methods struggle to capture complex concurrent causal relationships and lack robustness to incomplete telecommunication event sequences.

  • Method

    RCCD combines duration-aware, topology-informed hyperedge causal attention with mask-based alternating optimization and self-supervised reconstruction for incomplete observations.

  • Results

    RCCD significantly outperforms existing state-of-the-art methods in causal-learning accuracy and robustness across synthetic and real-world datasets.

  • Takeaways & Limitations

    RCCD provides a causal-discovery approach for large-scale telecommunication event sequences involving concurrent events and missing observations.

  • Takeaways & Limitations

    Reproduction inconsistencies and parameter-tuning deviations for some baselines may affect comparison fairness to some extent.

Abstract

from arXiv · show

Causal discovery on topological event sequences is crucial for ensuring the reliability of networks. However, existing methods struggle to capture the complex causal relationships arising from concurrent events and lack robustness to incomplete event sequences. To address these issues, we propose a resilient concurrent causal discovery method, termed RCCD, enabling robust learning of causal graphs from topological event sequences. Specifically, we first introduce an influence-aware hyperedge causal attention mechanism, which incorporates event duration into the embedding representation, aggregates concurrent event features via hyperedge causal convolution, and injects network prior knowledge to capture the complex many-to-one causal interactions. Furthermore, we design a masked-based alternating causal optimization framework, which forces the model to recover masked event types based on context through self-supervised mask reconstruction, thereby enhancing the resilience of the predictor to missing data. To validate the effectiveness of our method, we conduct extensive experiments on both simulated and real-world telecommunication network datasets. Experimental results demonstrate that the proposed method significantly outperforms existing state-of-the-art methods in both accuracy and robustness, making it more suitable for real-world telecommunication network environments.

I. INTRODUCTION

Telecommunication event sequences encode topology-constrained, concurrent, duration-dependent alarms, yet missing observations challenge causal discovery. RCCD addresses these challenges with topology-aware attention and mask-based alternating optimization, and experiments evaluate its accuracy and robustness.

  • Telecommunication alarms form chronological event sequences that can help locate root causes, block chain reactions, and trace anomaly propagation.
  • Concurrent alarms, duration effects, heterogeneous devices, topology constraints, and missing records create complex causal-learning conditions.
  • Existing methods struggle to model collaborative concurrent causality and generally assume complete event sequences.
  • RCCD introduces influence-aware hyperedge causal attention that encodes duration, aggregates concurrent events, and incorporates topology priors.
  • RCCD uses mask-based alternating causal optimization with self-supervised reconstruction to improve prediction robustness under incomplete observations.
  • Experiments on synthetic and real-world datasets assess RCCD's causal-learning performance and robustness against existing methods.

II. RELATED WORK

Related work spans topology-agnostic and topology-aware causal discovery, including statistical and neural point-process methods. Despite advances in temporal and causal attention, existing approaches incompletely address missing events, many-to-one causality, topology priors, and concurrent relationships.

  • A. Causal Learning on Event Sequences: Event-sequence causal discovery methods are classified as topology-agnostic or topology-aware according to whether network structure guides causal learning.
  • A. Causal Learning on Event Sequences: Topology-agnostic methods assume independently and identically distributed sequences, while topology-aware methods restrict causal inference using physical device adjacency.
  • A. Causal Learning on Event Sequences: Topology-aware statistical methods use Hawkes-process modeling, sparsity, search, or segmentation, but StateHPs remains dependent on complete events within segments.
  • A. Causal Learning on Event Sequences: Neural methods use temporal dependencies, causal weight matrices, topology constraints, and alternating optimization to learn event-sequence causal graphs.
  • B. Temporal Causal Attention Mechanism: Temporal attention research includes self-attention, Hawkes-process hybrids, sparse attention, and hierarchical propagation for modeling event dependencies.
  • B. Temporal Causal Attention Mechanism: Existing attention-based approaches remain limited for non-i.i.d. discrete event sequences because they often neglect topology priors and concurrent-event causality.

III. PROBLEM FORMULATION

The paper formulates causal discovery for telecommunication event sequences using network topology and seeks a binary causal graph, then presents RCCD's topology-aware, duration- and concurrency-sensitive architecture with masked optimization.

  • III. PROBLEM FORMULATION: The network is modeled as an undirected graph whose physical connections define topological relationships among nodes.
  • III. PROBLEM FORMULATION: Event types are represented by a directed acyclic graph and binary causal matrix, where each matrix entry indicates whether one type causes another.
  • III. PROBLEM FORMULATION: Each event records timestamp, type, topological node, and nonnegative duration within a sequence of length L.
  • III. PROBLEM FORMULATION: The stated goal is to infer the causal relationships among event types from observed events and network topology, producing the final binary causal matrix.
  • A. Overview: RCCD combines duration-, concurrency-, and topology-aware attention with masked multi-step optimization to discover a causal graph robustly from non-i.i.d. sequences.
  • A. Overview: IHCA encodes duration, distinguishes instantiated events, and aggregates consecutive local events into hyperedge representations for concurrent causal modeling.
  • A. Overview: MACO masks historical events during predictor training, reconstructs their types from context, and alternately optimizes predictor and causal parameters.
  • A. Overview: The overall pipeline combines event and topology processing, hyperedge causal attention, causal and k-hop constraints, topology decay, and alternating optimization.

B. Influence-aware Hyperedge Causal Attention Mechanism

IHCA enriches event representations with duration information alongside event type and occurrence time, while suppressing duration features for instantaneous events.

  • 1) Event Influence-Aware Encoding:: Duration is encoded as a learnable feature alongside occurrence time and event type to represent its influence on propagation.
  • 1) Event Influence-Aware Encoding:: A gating indicator incorporates duration only when d_i > 0, assigning instantaneous events a zero duration embedding.
  • 1) Event Influence-Aware Encoding:: The complete event embedding sums event-type, occurrence-time, and duration components.

2) Hyperedge Causal Attention Score:

The hyperedge causal attention mechanism replaces isolated pairwise attention with causal convolution over local event histories and applies causal and topological priors to constrain information flow.

  • 2) Hyperedge Causal Attention Score:: Standard self-attention relies on Query-Key similarity, which cannot represent joint causal effects from multiple concurrent events.
  • 2) Hyperedge Causal Attention Score:: Each attention head projects event embeddings into Query, Key, and Value representations using separate linear transformations.
  • 2) Hyperedge Causal Attention Score:: Depthwise causal convolution aggregates current and preceding events into hypernodes while preserving original information through residual connections.
  • 2) Hyperedge Causal Attention Score:: The resulting attention transfers aggregated historical information with adaptive weights, capturing pairwise similarity and local cooperative effects.
  • 3) Topology-Constrained Causal Attention Mechanism:: Topology-constrained attention combines hyperedge attention with a learnable causal graph and topology decay based on event-node distance.
  • 3) Topology-Constrained Causal Attention Mechanism:: The final attention output is a weighted sum of enhanced Value representations using topology-constrained attention scores.
  • 3) Topology-Constrained Causal Attention Mechanism:: The mechanism retains event pairs allowed by the causal graph and topologically close while preserving temporal causality.
  • 2) Hyperedge Causal Attention Score:: Outputs from multiple heads are concatenated, linearly transformed, normalized, and passed to a feedforward network before next-event prediction.

C. Mask-based Alternation Causal Optimization

MACO improves resilience to incomplete event sequences by masking eligible historical events during predictor training and reconstructing their types from context within alternating causal optimization.

  • C. Mask-based Alternation Causal Optimization: The existing EM-style framework alternates predictor training with causal-graph optimization, but incorrect temporal dependencies can create spurious edges.
  • C. Mask-based Alternation Causal Optimization: MACO masks historical events during the predictor's E-step and adds reconstruction so masked event types must be recovered from context.
  • 1) Mask Generation Strategy:: An event sequence contains timestamp, type, node, and duration attributes for L alarm events.
  • 1) Mask Generation Strategy:: The mask matrix marks positions for masking, subject to batch indexing and sequence-length constraints.
  • 1) Mask Generation Strategy:: Padding positions are excluded because event type 0 does not represent a real event.
  • 1) Mask Generation Strategy:: The final valid position is excluded because it serves as the prediction target needed to compute training loss.
  • 1) Mask Generation Strategy:: Each valid eligible position is independently masked with probability p, and a dedicated mask token replaces its event type.

2) EM-Style Two-Stage Alternating Optimization Framework:

RCCD uses an EM-style alternating framework that trains a predictor for event and masked-event reconstruction, then optimizes causal graph parameters with the predictor fixed. The four-task objective is intended to improve causal discovery stability under missing data.

  • The E-step fixes causal weights, topology decay, and adjacency inputs while the predictor processes masked event types, times, nodes, and durations.
  • The transformer predictor outputs the next event type, next time interval, and reconstructed types at masked positions.
  • The predictor combines intensity likelihood, event type, time interval, and mask reconstruction losses.The intensity loss models event occurrence from Hawkes-process intensity, while type and interval losses improve category and timing prediction.
  • Mask reconstruction minimizes the negative log probability of true event types at masked positions, using contextual information to complete missing events.
  • The jointly optimized predictor learns representations robust to missing data and improves the stability and accuracy of causal discovery.
  • In the M-step, predictor parameters are fixed while causal weights and topology decay are optimized using the summarized loss function.

3) Causal Judgment:

After alternating training, RCCD converts learned causal probabilities into a binary causal graph using a threshold. The experiments cover stationary causal learning, incomplete observations, hyperparameters, ablations, and a real-world case study.

  • RCCD declares a causal edge from vi to vj when the learned causal probability ω(Ãi,j) exceeds threshold ρ.
  • Topology decay is incorporated into attention weights so RCCD jointly learns causal probabilities and topological structure.
  • The evaluation includes baseline comparisons, incomplete-observation robustness, hyperparameter analysis, ablations, and a real-world causal-graph case study.
  • Synthetic datasets vary event types, physical devices, causal strength, and event counts, with ground-truth causal and topology graphs generated for benchmarking.
  • The real-world microwave datasets contain 24 or 25 event types, 439 or 474 nodes, and 64,599 or 48,573 event records.

B. Baselines

RCCD is compared with classical, neural, point-process, topology-aware, and large-language-model baselines using standard causal-graph metrics. It achieves strong F1 and SHD performance across synthetic and real-world datasets.

  • Baselines: Baselines include PC, GraNDAG, CORL, THPs, TNPAR, S2GCSL, CausalNET, and TCCD, alongside DeepSeek-v3.2, Gemini-v3.0, and ChatGPT-v5.1.
  • Evaluation Criteria: Causal graphs are evaluated with Precision, Recall, F1 Score, and Structural Hamming Distance.SHD counts the minimum edge insertions, deletions, or reversals needed to transform the predicted graph into the ground truth.
  • Stable datasets: RCCD achieves the best or second-best F1 Score on all stable datasets and the lowest SHD on synthetic datasets.
  • Stable datasets: On 15V-30N-Synthetic, RCCD reaches F1 0.8421 versus 0.6364 for CausalNET, 0.6429 for THPs, and 0.4615 for TCCD.
  • Stable datasets: On 20V-40N-Synthetic, RCCD reaches F1 0.8750 versus 0.6341 for CausalNET and 0.8649 for THPs.
  • Stable datasets: RCCD achieves the highest F1 on real-world datasets, including F1 0.5313 on 24V-439N-Microwave and 0.4967 on 25V-474N-Microwave.
  • Stable datasets: RCCD records SHD 3 versus 6 for CausalNET, 10 for THPs, and 21 for TCCD on 15V-30N-Synthetic, and SHD 4 versus 15 and 5 on 20V-40N-Synthetic.
  • Large language models: RCCD surpasses Gemini, DeepSeek, and ChatGPT in F1 Score on every dataset, including F1 0.8421 on 15V-30N-Synthetic.

F. Performance Comparison on Observing Incomplete Sequences

RCCD maintains leading causal-discovery performance as event-missing rates increase from 5% to 20%. Its F1 Score declines modestly and its SHD remains comparatively stable across synthetic and real telecommunication datasets.

  • Incomplete observations: Robustness is tested by randomly removing events at 5%, 10%, 15%, and 20% rates from two synthetic and two real telecommunication datasets.
  • Incomplete observations: RCCD maintains the highest F1 Score under all tested event-missing conditions.
  • F1 Score: On 15V-30N-Synthetic, RCCD’s F1 changes from 0.8421 without missing noise to 0.8235 at 20% missingness.
  • Overall robustness: Across synthetic and real telecommunication data, RCCD retains leading F1 and stable SHD while preserving a balance between precision and recall.
  • Structural Hamming Distance: On 15V-30N-Synthetic, RCCD’s SHD remains 3 from no missing noise to 20% missingness, versus 9 for THPs, 14 for CausalNET, and 85 for TCCD.
  • Structural Hamming Distance: On 20V-40N-Synthetic, RCCD’s SHD increases from 4 to 7 at 20% missingness, while THPs increases from 5 to 9 and CausalNET from 15 to 23.

G. Hyperparameters Sensitivity Analysis

RCCD maintains stable causal-discovery performance across tested regularizer settings, with minimal fluctuations on real-world data. Its complementary IHCA and MACO components improve performance under complete and incomplete observations.

  • Sparsity regularizer σ1: On synthetic datasets, changing σ1 from 0.1 to 0.3 leaves precision, recall, F1 Score, and SHD unchanged.On the 24V-439N-Microwave dataset, F1 changes from 0.5313 to 0.5274 across the same σ1 range.
  • Acyclicity regularizer σ2: For σ2 on 15V-30N-Synthetic, F1 remains 0.8421 and SHD remains 3 as σ2 increases from 0.1 to 0.3.On 20V-40N-Synthetic, F1 changes from 0.8750 to 0.8235 and SHD from 4 to 6 between σ2 = 0.1 and 0.2.
  • Hyperparameter sensitivity: RCCD maintains stable high performance across tested sparsity and acyclicity regularizer settings, indicating low hyperparameter sensitivity.The evaluation varies σ1 and σ2 from 0.1 to 0.3 across synthetic and real-world datasets.
  • Ablation study: IHCA mainly improves recall and F1, whereas MACO helps preserve structural accuracy and precision under incomplete observations.The paper attributes the optimal performance across test conditions to combining both components.

VI. DISCUSSION

RCCD combines duration- and concurrency-aware causal attention with masked alternating optimization to learn causal graphs from incomplete event sequences. Experiments report improved causal discovery accuracy and robustness, while the authors identify nonrandom missingness and baseline-reproduction differences as limitations.

  • Method: IHCA incorporates event duration and aggregates local concurrent events into hyper-edges to capture jointly triggered causal relationships.The mechanism uses a nonlinear gated mapping for duration and causal convolution for local concurrent-event aggregation.
  • Limitations: The masking strategy uses predefined random probabilities, which may not adapt fully to nonrandom event missingness in telecommunications networks.The authors propose learning the masking distribution from realistic collection noise in future work.
  • Limitations: Reproduction differences in text interpretation or parameter tuning may affect the fairness of comparisons for methods without released source code.TNPAR and TCCD were reproduced from their paper descriptions rather than official implementations.
  • Method: MACO improves robustness to missing events through self-supervised reconstruction within a mask-based alternating optimization framework.The framework enhances predictor robustness to incomplete observations while jointly optimizing causal structure learning.
  • Empirical effectiveness: RCCD significantly outperforms existing state-of-the-art methods in discovery performance and robustness across synthetic and real datasets.The reported evaluation covers multiple datasets and incomplete-observation settings.
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