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Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 7.0Download Report PDF
Hawkes processescausal discoverylatent subprocess modelstructure learningtime series
Abstract:

Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed subprocesses, real-world systems are often only partially observed, with latent subprocesses posing significant challenges. In this paper, we show that continuous-time event sequences can be represented by a discrete-time causal model as the time interval shrinks, and we leverage this insight to establish necessary and sufficient conditions for identifying latent subprocesses and the causal influences. Accordingly, we propose a two-phase iterative algorithm that alternates between inferring causal relationships among discovered subprocesses and uncovering new latent subprocesses, guided by path-based conditions that guarantee identifiability. Experiments on both synthetic and real-world datasets show that our method effectively recovers causal structures despite the presence of latent subprocesses.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
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Overview

Overall Novelty Assessment

The paper contributes a discrete-time causal representation of continuous-time Hawkes processes and establishes identifiability conditions for latent subprocesses via rank constraints. It resides in the 'Theoretical Foundations for Latent Confounder Identification' leaf, which contains only two papers total. This leaf sits within the broader 'Causal Structure Identification with Latent Confounders' branch, indicating a relatively sparse research direction focused on theoretical guarantees rather than algorithmic development or domain applications. The small sibling count suggests this is an emerging area with limited prior theoretical work.

The taxonomy reveals neighboring leaves addressing related but distinct challenges. The 'Algorithmic Approaches for Deconfounding High-Dimensional Networks' leaf focuses on computational methods for learning networks with hidden nodes, while 'Observable Network Learning and Granger Causality' assumes full observability or treats noise as the primary challenge. The paper's theoretical focus on identifiability conditions distinguishes it from these algorithmic and fully-observable settings. The taxonomy's scope notes clarify that this work excludes empirical methods without guarantees and settings where all processes are observed, positioning it at the intersection of causal inference theory and partially observed systems.

Among 21 candidates examined across three contributions, the discrete-time representation shows the most substantial prior work: 10 candidates examined with 2 appearing to provide overlapping results. The identifiability conditions contribution examined only 1 candidate with no clear refutation, while the two-phase algorithm examined 10 candidates with none refuting its novelty. This pattern suggests the discrete-time representation may build on established connections between continuous and discrete models, whereas the identifiability conditions and algorithmic contributions appear less anticipated by the limited search. The analysis explicitly covers top-K semantic matches plus citation expansion, not an exhaustive literature review.

Given the sparse taxonomy leaf and limited search scope, the work appears to address a theoretically underexplored problem. The identifiability conditions and algorithm contributions show minimal overlap among examined candidates, though the discrete-time representation connects to existing frameworks. The analysis reflects what 21 semantically similar papers reveal, leaving open whether broader searches across causal inference or point process literature would uncover additional related work. The theoretical focus and sparse leaf placement suggest meaningful novelty within the examined scope.

Taxonomy

Core-task Taxonomy Papers
11
3
Claimed Contributions
21
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: causal structure learning in partially observed Hawkes processes. The field addresses how to recover causal relationships among event sequences when only a subset of processes is observed, a challenge that arises naturally in social networks, neuroscience, and cybersecurity. The taxonomy organizes work into four main branches. The first branch, Causal Structure Identification with Latent Confounders, develops theoretical foundations and identifiability conditions for recovering causal graphs when unobserved processes confound the observed ones. The second branch, Observable Network Learning and Granger Causality, focuses on methods that infer directed influence networks from fully or partially observed data, often leveraging Granger-style causality tests and optimization-based discovery. The third branch, Causal Inference for Individual Events and Pairs, zooms in on finer-grained questions such as attributing specific events to their causes or learning from very few observed events. The fourth branch, Domain Applications and Extensions, explores how these techniques adapt to specialized settings like social media dynamics, wireless networks, and reinforcement learning. A central tension runs through the literature: methods that assume full observability (for example, High Dimensional Discovery[3] and Granger Optimal Intervention[4]) can exploit rich statistical structure but may fail when latent confounders are present, while approaches that explicitly model hidden processes must grapple with identifiability and computational complexity. Hawkes Latent Confounders[0] sits squarely in the first branch, providing theoretical guarantees for identifying causal structure even when confounding processes remain unobserved. This contrasts with works like Local Independence Testing[2], which also addresses partial observability but emphasizes testing conditional independence rather than full graph recovery. Meanwhile, domain-driven studies such as BlackLivesMatter Hawkes[9] and Wireless Topology Inference[5] illustrate how these foundational ideas translate into real-world inference tasks, though they often rely on domain-specific assumptions that may not hold universally.

Claimed Contributions

Discrete-time linear causal representation of Hawkes processes

The authors establish that multivariate Hawkes processes admit a linear autoregressive representation in discrete time as the bin width approaches zero. This theoretical result enables the use of second-order statistics to infer causal structure from discretized event counts.

10 retrieved papers
Can Refute
Identifiability conditions for latent subprocesses via rank constraints

The authors derive necessary and sufficient conditions based on rank constraints of cross-covariance matrices that enable identification of latent confounder subprocesses and causal relationships in partially observed Hawkes processes, without prior knowledge of latent components.

1 retrieved paper
Two-phase iterative discovery algorithm

The authors develop an algorithm that iteratively identifies causal relations among known subprocesses and discovers new latent confounders using path-based rank conditions. The method requires no prior specification of the number or existence of latent subprocesses.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Discrete-time linear causal representation of Hawkes processes

The authors establish that multivariate Hawkes processes admit a linear autoregressive representation in discrete time as the bin width approaches zero. This theoretical result enables the use of second-order statistics to infer causal structure from discretized event counts.

Contribution

Identifiability conditions for latent subprocesses via rank constraints

The authors derive necessary and sufficient conditions based on rank constraints of cross-covariance matrices that enable identification of latent confounder subprocesses and causal relationships in partially observed Hawkes processes, without prior knowledge of latent components.

Contribution

Two-phase iterative discovery algorithm

The authors develop an algorithm that iteratively identifies causal relations among known subprocesses and discovers new latent confounders using path-based rank conditions. The method requires no prior specification of the number or existence of latent subprocesses.

Table of Contents