Haoyu Wei
arXiv 15 Sep 2026 · Mathematics — Statistics Theory
arXiv:2609.17939 · PDF · Extracted main text
Exploiting the equality restrictions that nested Markov models encode requires their tangent-space geometry. For strictly positive finite-state models on arbitrary acyclic directed mixed graphs (ADMGs), we differentiate the recursive-head chart and prove that the range of its score map is the full tangent space. Intrinsic-set coordinate blocks form an algebraic direct sum, blocks of distinct districts are orthogonal, and the resulting Gram projection needs neither mb-shieldedness nor a district order. Exact counterexamples show that observational centering and kernel normalization alone do not certify tangency. For the node, complete-source edge, and compatible path-specific intervention targets considered here, boundary substitution yields a normalized configured active law and an order-free canonical-gradient formula, extended to finite mixtures by independent source redraws. A coherent one-step estimator with an exact remainder identity and a model-valid chart-flow targeted maximum likelihood estimator are efficient under stated local conditions. On a narrower source-isolated fixed-node subclass, a sequential estimator has an exact transition-factorized drift and up to $2^m$ nuisance-correctness regimes over $m$ active-district transitions; its all-correct influence function projects onto the canonical gradient, and an exact rational law exhibits a strict variance gap. These results separate order-free efficiency on arbitrary finite-state ADMGs from multiple robustness of a narrower construction.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bhattacharya, Rohit and Nabi, Razieh and Shpitser, Ilya (2022) Semiparametric inference for causal effects in graphical models with hidden variables | 1.000 | 7 | 4 | 100% |
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| 3 | Evans, Robin J (2018) Margins of discrete Bayesian networks | 0.843 | 4 | 3 | 75% |
| 4 | Shpitser, Ilya (2013) Counterfactual graphical models for longitudinal mediation analysis with unobserved confounding | 0.843 | 4 | 3 | 75% |
| 5 | Shpitser, Ilya and Tchetgen Tchetgen, Eric J (2016) Causal inference with a graphical hierarchy of interventions | 0.843 | 4 | 3 | 75% |
| 6 | Evans, Robin J and Richardson, Thomas S (2019) Smooth, identifiable supermodels of discrete DAG models with latent variables | 0.757 | 53 | 5 | 43% |
| 7 | Zhou, Xiang (2022) Semiparametric estimation for causal mediation analysis with multiple causally ordered mediators | 0.737 | 3 | 3 | 67% |
| 8 | Richardson, Thomas S and Evans, Robin J and Robins, James M and Shpi… (2023) Nested Markov properties for acyclic directed mixed graphs | 0.705 | 40 | 5 | 35% |
| 9 | van der Laan, Mark J. and Gruber, Susan (2016) One-Step Targeted Minimum Loss-Based Estimation Based on Universal Least Favorable One-Dimensional Submodels | 0.644 | 2 | 2 | 100% |
| 10 | Avin, Chen and Shpitser, Ilya and Pearl, Judea (2005) Identifiability of path-specific effects | 0.405 | 1 | 1 | 100% |
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