A Data-driven Two-phase Multi-split Causal Ensemble Model for Time Series

Zhipeng Ma, Marco Kemmerling*, Daniel Buschmann, Chrismarie Enslin, Daniel Lütticke, Robert H. Schmitt

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Causal inference is a fundamental research topic for discovering the cause–effect relationships in many disciplines. Inferring causality means identifying asymmetric relations between two variables. In real-world systems, e.g., finance, healthcare, and industrial processes, time series data from sensors and other data sources offer an especially good basis to infer causal relationships. Therefore, many different time series causal inference algorithms have been proposed in recent years. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to identify linear relationships, while others are applicable for non-linearities. Algorithms further vary in their sensitivity to noise and their ability to infer causal information from coupled vs. non-coupled time series. As a consequence, different algorithms often generate different causal relationships for the same input. In order to achieve a more robust causal inference result, this publication proposes a novel data-driven two-phase multi-split causal ensemble model to combine the strengths of different causality base algorithms. In comparison to existing approaches, the proposed ensemble method reduces the influence of noise through a data partitioning scheme in a first phase. To achieve this, the data are initially divided into several partitions and the base causal inference algorithms are applied to each partition. Subsequently, Gaussian mixture models are used to identify the causal relationships derived from the different partitions that are likely to be valid. In the second phase, the identified relationships from each base algorithm are then merged based on three combination rules. The proposed ensemble approach is evaluated using multiple metrics, among them a newly developed evaluation index for causal ensemble approaches. We perform experiments using three synthetic datasets with different volumes and complexity, which have been specifically designed to test causality detection methods under different circumstances while knowing the ground truth causal relationships. In these experiments, our causality ensemble outperforms each of its base algorithms. In practical applications, the use of the proposed method could hence lead to more robust and reliable causality results.
Original languageEnglish
Article number982
Issue number5
Publication statusPublished - 26. Apr 2023


  • Causal inference
  • Ensemble learning
  • Time series
  • Asymmetry


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