  One of the fundamental challenges found throughout the data sciences is to
explain why things happen in specific ways, or through which mechanisms a
certain variable $X$ exerts influences over another variable $Y$. In statistics
and machine learning, significant efforts have been put into developing
machinery to estimate correlations across variables efficiently. In causal
inference, a large body of literature is concerned with the decomposition of
causal effects under the rubric of mediation analysis. However, many variations
are spurious in nature, including different phenomena throughout the applied
sciences. Despite the statistical power to estimate correlations and the
identification power to decompose causal effects, there is still little
understanding of the properties of spurious associations and how they can be
decomposed in terms of the underlying causal mechanisms. In this manuscript, we
develop formal tools for decomposing spurious variations in both Markovian and
Semi-Markovian models. We prove the first results that allow a non-parametric
decomposition of spurious effects and provide sufficient conditions for the
identification of such decompositions. The described approach has several
applications, ranging from explainable and fair AI to questions in epidemiology
and medicine, and we empirically demonstrate its use on a real-world dataset.
