Notes on Forré's Notion of Conditional Independence and Causal Calculus for Continuous Variables
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917361592827904 |
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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 |
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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 |