Algebraic Constraints for Linear Acyclic Causal Models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915368238317568 |
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| author | Gigliotti, Cole Robeva, Elina |
| author_facet | Gigliotti, Cole Robeva, Elina |
| contents | In this paper we study the space of second- and third-order moment tensors of random vectors which satisfy a Linear Non-Gaussian Acyclic Model (LiNGAM). In such a causal model each entry $X_i$ of the random vector $X$ corresponds to a vertex $i$ of a directed acyclic graph $G$ and can be expressed as a linear combination of its direct causes $\{X_j: j\to i\}$ and random noise. For any directed acyclic graph $G$, we show that a random vector $X$ arises from a LiNGAM with graph $G$ if and only if certain easy-to-construct matrices, whose entries are second- and third-order moments of $X$, drop rank. This determinantal characterization extends previous results proven for polytrees and generalizes the well-known local Markov property for Gaussian models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_00215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic Constraints for Linear Acyclic Causal Models Gigliotti, Cole Robeva, Elina Statistics Theory 62R01, 62H22 In this paper we study the space of second- and third-order moment tensors of random vectors which satisfy a Linear Non-Gaussian Acyclic Model (LiNGAM). In such a causal model each entry $X_i$ of the random vector $X$ corresponds to a vertex $i$ of a directed acyclic graph $G$ and can be expressed as a linear combination of its direct causes $\{X_j: j\to i\}$ and random noise. For any directed acyclic graph $G$, we show that a random vector $X$ arises from a LiNGAM with graph $G$ if and only if certain easy-to-construct matrices, whose entries are second- and third-order moments of $X$, drop rank. This determinantal characterization extends previous results proven for polytrees and generalizes the well-known local Markov property for Gaussian models. |
| title | Algebraic Constraints for Linear Acyclic Causal Models |
| topic | Statistics Theory 62R01, 62H22 |
| url | https://arxiv.org/abs/2505.00215 |