Causal Ordering for Structure Learning From Time Series

2025-10-28

AI Summary

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.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Predicting causal structure from time series data is crucial for understanding complex phenomena in physiology, brain connectivity, climate dynamics, and socio-economic behaviour. Causal discovery in time series is hindered by the combinatorial complexity of identifying true causal relationships, especially as the number of variables and time points grow. A common approach to simplify the task is the so-called ordering-based methods. Traditional ordering methods inherently limit the representational capacity of the resulting model. In this work, we fix this issue by leveraging multiple valid causal orderings, instead of a single one as standard practice. We propose DOTS (Diffusion Ordered Temporal Structure), using diffusion-based causal discovery for temporal data. By integrating multiple orderings, DOTS effectively recovers the transitive closure of the underlying directed acyclic graph, mitigating spurious artifacts inherent in single-ordering approaches. We formalise the problem under standard assumptions such as stationarity and the additive noise model, and leverage score matching with diffusion processes to enable efficient Hessian estimation. Extensive experiments validate the approach. Empirical evaluations on synthetic and real-world datasets demonstrate that DOTS outperforms state-of-the-art baselines, offering a scalable and robust approach to temporal causal discovery. On synthetic benchmarks ($d{=}!3-!6$ variables, $T{=}200!-!5{,}000$ samples), DOTS improves mean window-graph $F1$ from $0.63$ (best baseline) to $0.81$. On the CausalTime real-world benchmark ($d{=}20!-!36$), while baselines remain the best on individual datasets, DOTS attains the highest average summary-graph $F1$ while halving runtime relative to graph-optimisation methods. These results establish DOTS as a scalable and accurate solution for temporal causal discovery.

Problem

• Addresses combinatorial complexity in time series causal discovery
• Overcomes limitations of single-ordering methods in structure learning
• Enhances scalability and accuracy for temporal causal relationships

Innovation

• Uses diffusion-based causal discovery for temporal data
• Integrates multiple valid causal orderings instead of one
• Leverages score matching with diffusion processes for efficiency