Lower Bounds on the Size of Markov Equivalence Classes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909705031385088 |
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| author | Jahn, Erik Eberhardt, Frederick Schulman, Leonard J. |
| author_facet | Jahn, Erik Eberhardt, Frederick Schulman, Leonard J. |
| contents | Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the case when any of these assumptions is relaxed. Specifically, we prove exponentially large lower bounds for the expected size of Markov equivalence classes in three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_20933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower Bounds on the Size of Markov Equivalence Classes Jahn, Erik Eberhardt, Frederick Schulman, Leonard J. Machine Learning Statistics Theory Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the case when any of these assumptions is relaxed. Specifically, we prove exponentially large lower bounds for the expected size of Markov equivalence classes in three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs. |
| title | Lower Bounds on the Size of Markov Equivalence Classes |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2506.20933 |