The Statistical Cost of Causal Discovery with Feedback
What determines the unavoidable sample cost of learning cyclic causal structure? For cyclic linear non-Gaussian models, we study exact condensation recovery from observational data: identifying the strongly connected component (SCC) partition and all edges between components. We establish the first information-theoretic lower bounds on sample complexity for this target. For $p$ variables, maximum SCC size $s_{\max}$, and maximum external-parent count $d_B$, any estimator requires order $s_{\max}\log(ep/s_{\max})+d_B\log(ep/d_B)$ samples in the worst case over a regular model class. These bounds distinguish the costs of SCC membership and external-parent selection. Under principal invertib...
| Authors | Sunmin Oh, Seungsu Han, Gunwoong Park |
|---|---|
| Primary category | stat.ML |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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