Marginal DAG Models Equivalent to Another DAG
Talkat Quantum Physics and Statistical Causal Models (Simons Institute workshop, 2022) · 2022-04-27..04-29·
summary
Claim: a marginal DAG model equals the marginal model of some DAG on the observed variables if and only if the original MDAG induces no non‑trivial inequality constraints. Proof builds explicit reductions: form the canonical DAG and latent projection, then enlarge safely using the maximal arid projection and the maximal ancestral projection while tracking nested constraints. Tools include intrinsic closures, discriminating paths and e‑separation; counterexamples always produce a Bell‑type or discriminating‑path inequality, so the construction successfully characterizes when equivalence holds.
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chapters (13)
- 0:00Introduction to DAG models
- 2:05Background and context
- 3:58Constraint types in DAGs
- 6:30Defining the main result
- 8:33Graphical representations
- 13:27Proof strategy and projections
- 17:41Intrinsic closure
- 21:24Arrow projection procedure
- 24:20Connecting constraints
- 28:31Ancestral projections
- 31:28Finalizing the proof
- 36:20Summary and conclusions
- 38:42Q&A and discussion
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