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In fields such as finance, climate science, and neuroscience, inferringcausal relationships from time series data poses a formidable challenge. Whilecontemporary techniques can handle nonlinear relationships between variablesand flexible noise distributions, they rely on the simplifying assumption thatdata originates from the same underlying causal model. In this work, we relaxthis assumption and perform causal discovery from time series data originatingfrom mixtures of different causal models. We infer both the underlyingstructural causal models and the posterior probability for each samplebelonging to a specific mixture component. Our approach employs an end-to-endtraining process that maximizes an evidence-lower bound for data likelihood.Through extensive experimentation on both synthetic and real-world datasets, wedemonstrate that our method surpasses state-of-the-art benchmarks in causaldiscovery tasks, particularly when the data emanates from diverse underlyingcausal graphs. Theoretically, we prove the identifiability of such a modelunder some mild assumptions.

Discovering Mixtures of Structural Causal Models from Time Series Data