Research map / Probabilistic and scientific modeling / Causal discovery
On Causal Discovery in the Presence of Deterministic Relations
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Shows exact score-based search handles deterministic relations under SMR, and proposes DGES, a three-phase causal discovery framework (minimal deterministic cluster detection, modified GES, exact search on deterministic clusters) with partial identifiability guarantees.
Problem
Causal discovery when some variables are deterministic functions of their parents (no noise), which violates faithfulness and breaks constraint-based methods like PC; exact score-based search is accurate but computationally expensive.
Approach
Detect minimal deterministic clusters, run a modified GES (ignoring spurious constant independencies, adjusted BIC/generalized score) globally, then run exact search (A*) only on deterministic clusters and their neighbors, giving efficiency while relying on SMR rather than faithfulness.
Key results
- On simulated data, DGES and exact A* generally outperform GES and DPC on SHD, F1, precision and recall across settings, with DGES runtime growing much more steadily than A*.
- On the PUMS census data, DGES recovers a sparser graph (5 edges) than GES (6 edges) and detects the deterministic AI-AAI relation, while PC returns an empty bridge set.
- On the pharmacokinetics data, DGES with generalized score detects at least three minimal deterministic clusters: {height, weight, BMI}, {kel, Vd, Clearance}, {kel, Thalf}.
Surprising findings
- Constraint-based PC yields an empty bridge set on the census data, attributed to faithfulness violation from determinism.
- GES performs better than DPC in the deterministic simulated settings.
Limitations
- Cannot identify skeleton and directions within the deterministic cluster part when deterministic variables overlap.
- Exact search in phase 3 is computationally expensive when many minimal deterministic clusters exist.
- Identifiability requires the condition |PA_i| < |MinDC| - 1 and SMR; otherwise the bridge set may not be uniquely identified.
Experimental setup
Datasets: pharmacokinetics dataset (Pharmacokinetics open database) US census PUMS (2021, preprocessed as in prior work)
Benchmarks: simulated linear Gaussian and nonlinear SCM datasets pharmacokinetics real-world data US census PUMS
Metrics: SHD F1 score precision recall runtime
Baselines: DPC GES A* PC
Builds on: GES A* exact search generalized score sparsest Markov representation PC algorithm
Closest papers by meaning
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- THE ROBUSTNESS OF DIFFERENTIABLE CAUSAL DISCOVERY IN MISSPECIFIED SCENARIOS (ICLR 2025 · similarity 0.89)
- Strong and Weak Identifiability of Optimization-based Causal Discovery in Non-linear Additive Noise Models (ICML 2025 · similarity 0.89)
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