A Transformational Characterization of Unconditionally Equivalent Bayesian Networks. (arXiv:2203.00521v3 [stat.ML] UPDATED)

We consider the problem of characterizing Bayesian networks up to
unconditional equivalence, i.e., when directed acyclic graphs (DAGs) have the
same set of unconditional $d$-separation statements. Each unconditional
equivalence class (UEC) is uniquely represented with an undirected graph whose
clique structure encodes the members of the class. Via this structure, we
provide a transformational characterization of unconditional equivalence; i.e.,
we show that two DAGs are in the same UEC if and only if one can be transformed
into the other …

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