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Causal inference is a fundamental research topic for discovering thecause-effect relationships in many disciplines. However, not all algorithms areequally well-suited for a given dataset. For instance, some approaches may onlybe able to identify linear relationships, while others are applicable fornon-linearities. Algorithms further vary in their sensitivity to noise andtheir ability to infer causal information from coupled vs. non-coupled timeseries. Therefore, different algorithms often generate different causalrelationships for the same input. To achieve a more robust causal inferenceresult, this publication proposes a novel data-driven two-phase multi-splitcausal ensemble model to combine the strengths of different causality basealgorithms. In comparison to existing approaches, the proposed ensemble methodreduces the influence of noise through a data partitioning scheme in the firstphase. To achieve this, the data are initially divided into several partitionsand the base algorithms are applied to each partition. Subsequently, Gaussianmixture models are used to identify the causal relationships derived from thedifferent partitions that are likely to be valid. In the second phase, theidentified relationships from each base algorithm are then merged based onthree combination rules. The proposed ensemble approach is evaluated usingmultiple metrics, among them a newly developed evaluation index for causalensemble approaches. We perform experiments using three synthetic datasets withdifferent volumes and complexity, which are specifically designed to testcausality detection methods under different circumstances while knowing theground truth causal relationships. In these experiments, our causality ensembleoutperforms each of its base algorithms. In practical applications, the use ofthe proposed method could hence lead to more robust and reliable causalityresults.

A Data-Driven Two-Phase Multi-Split Causal Ensemble Model for Time Series