Notes on Forré's Notion of Conditional Independence and Causal Calculus for Continuous Variables

Fuente: arXiv
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Auteur principal: Chen, Leihao
Format: Preprint
Publié: 2026
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author Chen, Leihao
author_facet Chen, Leihao
contents Recently, Forré (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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_24333
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Notes on Forré's Notion of Conditional Independence and Causal Calculus for Continuous Variables
Chen, Leihao
Statistics Theory
Probability
Methodology
Machine Learning
Recently, Forré (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.
title Notes on Forré's Notion of Conditional Independence and Causal Calculus for Continuous Variables
topic Statistics Theory
Probability
Methodology
Machine Learning
url https://arxiv.org/abs/2603.24333