generate causal temporal graphs

Real-world time-series generation faces critical bottlenecks, including causal structure distortion and inadequate modeling of dynamic lags. Method: We propose a three-stage causal simulation framework: (i) lag-aware causal graph estimation, (ii) nonlinear functional dependency approximation via neural ODEs or MLPs, and (iii) joint noise distribution modeling using a VAE-GAN hybrid. Our approach introduces the first model-agnostic, customizable time-series causal generation pipeline, augmented by a min-max AutoML-driven adversarial discriminative optimization mechanism and a multi-dimensional evaluation paradigm balancing fidelity and verifiability. Contribution/Results: Experiments on real, semi-synthetic, and synthetic datasets demonstrate substantial improvements in causal fidelity and temporal plausibility of generated sequences. The method achieves superior generalization in downstream causal inference and intervention modeling tasks, outperforming existing baselines in both qualitative and quantitative assessments.

Existing time series benchmarks lack interventional data, hindering the training of causal foundation models. To address this gap, this work proposes CausalTimePrior, a framework that introduces the first synthetic time series structural causal model (TSCM) capable of generating paired observational and interventional data. The framework supports configurable causal graphs, nonlinear autoregressive mechanisms, state-switching dynamics, and diverse intervention types—including hard, soft, and time-varying interventions. Prior-data fitting networks (PFNs) trained within this framework demonstrate effective in-context estimation of causal effects on unseen TSCMs, underscoring the framework’s pivotal role in advancing causal foundation models for time series.

Current time-series causal discovery lacks benchmark datasets that simultaneously incorporate ground-truth causal graphs and realistic temporal characteristics—particularly systematic modeling of nonstationarity (trends/seasonality), irregular sampling, and unobserved confounding. To address this gap, we propose the first comprehensive synthetic benchmark suite, generating linear and nonlinear time-series data via structural equation models. Our framework explicitly incorporates stochastic trends, periodic components, sparse causal graphs, heterogeneous noise (Gaussian, heavy-tailed, heteroscedastic), and controllable latent confounders, while orthogonally decoupling causal graph density from noise distribution. The suite provides dual versions of each causal graph—with and without confounding—for rigorous evaluation. Extensive experiments on state-of-the-art algorithms (PCMCI+, LPCMCI, FGES) reveal substantial performance degradation under nonstationary and confounded settings. All code, data-generation scripts, and standardized evaluation protocols are publicly released.

Existing static network models fail to capture causal evolution and historical dependencies driven by temporal events in dynamic networks. To address this, we propose a generative model based on a modified Hawkes process that— for the first time—explicitly incorporates learnable time-varying covariates (e.g., dynamic graph features) into the intensity function, enabling unified modeling of heterogeneous edge activation processes. To improve simulation efficiency, we design an adaptive thinning algorithm for fast, unbiased sampling of continuous-time point processes. Furthermore, we introduce the first systematic evaluation framework tailored to dynamic network generation. Experiments on diverse real-world and synthetic datasets demonstrate state-of-the-art fidelity, with inference speedups of 3–5× over baselines, significantly enhancing scalability and practical applicability.

Modeling dynamic, non-stationary causal structures in complex systems remains challenging due to evolving temporal dependencies and heterogeneous causal mechanisms. Method: This paper proposes the first differentiable time-varying causal graph synthesis framework for end-to-end learning of dynamic causal mechanisms with time lags and conditional dependencies. It integrates structural equation models, neural differential equations, and temporal graph neural networks, incorporating a learnable time-varying adjacency matrix and a causal lag mask to explicitly capture the evolution and heterogeneity of temporal causality. Contribution/Results: The method achieves a 12.6% improvement in causal discovery accuracy across multiple benchmark datasets. Moreover, it enables controllable generation of counterfactual time series and fine-grained prediction of intervention responses, establishing a unified, differentiable paradigm for dynamic causal inference and generation.

Existing approaches evaluate temporal link prediction models solely based on predictive accuracy, which fails to verify whether these models capture genuine causal mechanisms. This work proposes the Causal Temporal Interaction Graph (CTIG) framework, which introduces—for the first time—a continuous-time structural equation model capable of representing both excitatory and inhibitory effects. The framework further develops a causal distance metric grounded in cross-model prediction errors, enabling quantifiable counterfactual causal evaluation. By integrating structural equation modeling, causal graph generation, and timestamp perturbation techniques, CTIG reveals significant performance degradation under controlled causal shifts, thereby effectively demonstrating its discriminative power in assessing a model’s capacity for causal reasoning.

Traditional temporal link prediction evaluation struggles to disentangle model error from the irreducible uncertainty inherent in the generative process, thereby obscuring whether a model has genuinely learned the underlying causal mechanisms. This work proposes a probabilistic causal temporal graph generation framework featuring transient edges and known causal structure, enabling joint assessment of causal parameter recovery and link prediction performance through a binary logistic model. By deriving the Cramér–Rao bound and analyzing Fisher information, the study reveals an intrinsic trade-off between parameter identifiability and prediction difficulty: higher identifiability corresponds to higher entropy, rendering individual link prediction fundamentally more challenging. Experimental results corroborate this theoretical trade-off, demonstrating that predictive accuracy alone is insufficient to gauge a model’s capacity to capture the true causal dynamics.

This work investigates how to extract the implicit directed, time-lagged causal dependency structure embedded within pretrained time series forecasting models to elucidate their decision-making rationale. To this end, the authors propose a model-agnostic post-hoc interpretability framework that, during inference, probes model responses through interventional input clamping to construct directed temporal influence signals. They further introduce Qbic, a sparsity-aware graph selection criterion that operates without requiring ground-truth graph labels, effectively balancing predictive fidelity with structural complexity. The approach is compatible with diverse time series model architectures and demonstrates strong generality across synthetic, simulated, and real-world benchmarks. Empirical evaluations show that the method achieves competitive structural accuracy while significantly improving the precision of temporal lag localization.

This work addresses a fundamental issue in graph representation learning: node aggregation operations violate core assumptions of causal inference, thereby compromising causal validity. To resolve this, the authors propose a causal modeling framework grounded in the graph’s minimal inseparable units, which rigorously ensures identifiability of the underlying causal structure. They further analyze the trade-offs and simplifying conditions required for exact causal modeling. Building on this theoretical foundation, they design a plug-in causal enhancement module compatible with existing graph learning pipelines. Experiments on controlled synthetic datasets validate the theoretical claims and demonstrate that the proposed approach substantially improves the model’s capacity for causal reasoning.

This study addresses causal inference under network interference, where existing methods typically rely on accurate knowledge of the interaction network—a requirement often unmet in real-world settings due to missing, incomplete, or noisy network data. To overcome this limitation, the authors propose a network-free causal message passing approach that leverages the temporal dynamics of outcome variables to estimate both total treatment effects and spillover effects. Evaluated on a large-scale real-world field experiment, the method is compared against a bipartite graph-based approach that requires network information. Results show that, even without any network data, the proposed method yields effect estimates directionally consistent with the network-aware baseline across all metrics and achieves statistically significant alignment on key decision-relevant outcomes. This work provides the first empirical validation in a real experiment that temporal dynamics alone can effectively substitute for observed network structure, thereby eliminating dependence on network information.