Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.02404 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918235008401408 |
|---|---|
| author | Alexandr, Yulia Dawson, Kristen Friedman, Hannah Mohammadi, Fatemeh Semnani, Pardis Yu, Teresa |
| author_facet | Alexandr, Yulia Dawson, Kristen Friedman, Hannah Mohammadi, Fatemeh Semnani, Pardis Yu, Teresa |
| contents | We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models, we show that this is a decomposition into radical ideals by displaying Gröbner bases for the components. We identify conditions under which the components are prime, and establish formulas for the dimensions of these prime ideals.
Moreover, we show that the components in the decomposition can be grouped into equivalence classes defined by their combinatorial structure, and we derive a closed formula for the number of such classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02404 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decomposing conditional independence ideals with hidden variables Alexandr, Yulia Dawson, Kristen Friedman, Hannah Mohammadi, Fatemeh Semnani, Pardis Yu, Teresa Commutative Algebra Combinatorics We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models, we show that this is a decomposition into radical ideals by displaying Gröbner bases for the components. We identify conditions under which the components are prime, and establish formulas for the dimensions of these prime ideals. Moreover, we show that the components in the decomposition can be grouped into equivalence classes defined by their combinatorial structure, and we derive a closed formula for the number of such classes. |
| title | Decomposing conditional independence ideals with hidden variables |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2505.02404 |