Notes on Forr\'e's Notion of Conditional Independence and Causal Calculus for Continuous Variables

Leihao Chen

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arXiv · 2603.24333

Notes on Forr\'e's Notion of Conditional Independence and Causal Calculus for Continuous Variables

Leihao Chen

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Abstract

Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes a strong global Markov property connecting transitional conditional independencies with suitable graphical separation criteria for directed mixed graphs with input nodes (iDMGs), together with a version of causal calculus for iDMGs in a general measure-theoretic setting. These notes aim to further illustrate the motivations behind this framework and its connections to the literature, highlight certain subtlies in the general measure-theoretic causal calculus, and extend the "one-line" formulation of the ID algorithm of Richardson et al. (Ann. Statist. 51(1):334--361, 2023) to the general measure-theoretic setting.

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Leihao Chen. 2026-03-25. Notes on Forr\'e's Notion of Conditional Independence and Causal Calculus for Continuous Variables. https://arxiv.org/abs/2603.24333

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