stage-aware causal ordering

Existing causal discovery methods often violate process priors in multi-stage settings, yielding counterintuitive results and struggling to scale efficiently to large datasets. To address these limitations, this work proposes a causal discovery framework that integrates stage-specific prior knowledge. The approach first employs a structure-knowledge-guided causal ordering algorithm to infer the causal sequence among variables and construct an initial causal graph. It then introduces an efficient pruning mechanism based on stochastic gated neural networks to eliminate spurious edges. Evaluated across multiple datasets, the proposed method significantly outperforms current state-of-the-art techniques, achieving both high accuracy in recovering the true causal structure and substantial gains in computational efficiency.

This paper addresses the limited expressiveness and combinatorial explosion in time-series causal discovery caused by reliance on a single causal ordering. We propose DOTS, a scalable diffusion-based framework that abandons the conventional single-order constraint by modeling multiple valid causal orderings. Leveraging score matching and efficient Hessian estimation, DOTS recovers the transitive closure of the underlying DAG under stationarity and additive noise assumptions, effectively suppressing spurious correlations. Experiments demonstrate that DOTS achieves an average window-graph F1-score of 0.81 (+18%) on synthetic data and attains the highest average summary-graph F1-score on the real-world CausalTime benchmark, while reducing runtime by 50% compared to mainstream graph-optimization methods. The core innovation lies in multi-order diffusion modeling, which overcomes the uniqueness limitation of causal ordering and enables high-accuracy, high-efficiency learning of temporal causal structures.

Global causal discovery from high-dimensional nonlinear observational data faces challenges in uniquely identifying the underlying DAG, while existing methods are hindered by the curse of dimensionality or restrictive parametric assumptions—such as linearity or additive noise. Method: This paper proposes a topological-sorting-driven hierarchical causal ordering framework. It is the first to encode ancestral relationships as a compact causal order and integrates local conditional set search with nonparametric conditional independence testing, thereby relaxing linearity and additive-noise constraints. Contribution/Results: We provide theoretical guarantees for correctness and polynomial-time complexity. Empirical evaluation on synthetic data demonstrates significantly higher edge identification accuracy than state-of-the-art methods, while maintaining compatibility with both linear and arbitrary nonlinear additive-noise models.

Existing methods predominantly rely on static or first-order causal assumptions, rendering them inadequate for capturing higher-order and time-varying dynamic causal dependencies in temporal point processes. To address this, we propose the first end-to-end differentiable framework that jointly models multi-order dynamic causal discovery and temporal point processes. Our approach introduces a learnable, time-varying directed acyclic graph (DAG) with parameterized edge weights, integrated into the intensity function parameterization; structural differentiability is ensured via sparsity and acyclicity constraints. By unifying gradient-based optimization with structural priors, the framework simultaneously learns both event generation mechanisms and latent time-evolving causal graphs. Extensive experiments on multiple real-world datasets demonstrate significant improvements in event prediction accuracy. Moreover, our method uncovers interpretable, higher-order causal pathways exhibiting temporal evolution—achieving both state-of-the-art predictive performance and strong causal interpretability.

Large language models (LLMs) and other imperfect experts often conflate direct and indirect causal effects and induce spurious cyclic dependencies when inferring causal graphs. Method: We propose using **causal order**—a more robust knowledge interface—instead of causal graphs, and design a **cycle-avoiding triplet prompting strategy**, integrating multi-round auxiliary-variable queries with a voting-based ensemble under constrained modeling to enhance ordinal consistency. Contribution/Results: We provide the first theoretical analysis and empirical validation demonstrating that causal order exhibits superior stability and noise robustness compared to causal graphs. Experiments show that lightweight models (e.g., Phi-3), when equipped with our framework, achieve **higher causal-order accuracy than GPT-4** across multiple real-world benchmarks, significantly reducing cyclic errors and improving robustness and precision in downstream causal discovery and effect estimation.

This work addresses the challenge of formalizing multiscale causal relationships in complex systems by proposing a concise discrete hierarchical causal modeling framework. The framework introduces causal classes to abstract cross-level causal influences and integrates aggregation operators with discrete event-time mappings to characterize how high-level actors constrain, select, and organize the behaviors of low-level agents. The resulting formalism comprises three core components—causal classes, aggregation mechanisms, and temporal mappings—providing a unified and computationally tractable foundation for hierarchical causal analysis in complex systems.

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 study addresses a critical limitation in the evaluation of causal discovery algorithms, which often rely on randomly generated directed acyclic graphs (DAGs) whose implicit topological properties may distort performance assessments. The authors observe that in common random DAG models—such as Erdős–Rényi and scale-free graphs—the number of “relatives” (nodes reachable via open paths) for each node strictly increases along the true causal order. They prove that this monotonicity property renders the Markov equivalence class degenerate, collapsing it to a single unique graph. Leveraging this insight, they propose a causal ordering recovery criterion based on estimating relative counts and introduce a corresponding time-ordered DAG sampling scheme. Experiments demonstrate that the method efficiently approximates the true causal order across diverse simulation settings, while also exposing inherent limitations in current synthetic data evaluation paradigms.

This work addresses the unreliability of in-context learning on tabular data under distribution shifts or interventions, which stems from overreliance on spurious correlations and the typical disconnect between causal discovery and predictive modeling. The authors propose TabOrder, the first framework to directly embed a learnable causal variable ordering into the prediction architecture. TabOrder infers a causal topological order via an unsupervised likelihood objective and restricts predictions to use only predecessor features in this causal sequence. It further introduces a causally constrained attention mechanism that jointly optimizes causal discovery, prediction, and missing value imputation. Theoretical analysis and experiments demonstrate that TabOrder accurately recovers causal orders, achieves strong performance in both prediction and imputation tasks, and yields interpretable insights on real-world biological intervention data.

本文通过比较条件协方差算子的范数，提出了一种新的方法来识别函数变量的有效拓扑排序，进而估计因果有向无环图。