Research map / Probabilistic and scientific modeling / Causal discovery
Differentiable Cyclic Causal Discovery Under Unmeasured Confounders
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Proposes DCCD-CONF, a differentiable likelihood-based method that learns nonlinear cyclic causal graphs with unmeasured confounders (modeled as correlated Gaussian noise) from interventional data, with a consistency result.
Problem
Causal discovery when the causal graph may contain directed cycles and there are unmeasured confounders, in nonlinear settings and using interventional data; existing methods are linear, acyclic, or unscalable.
Approach
Model nonlinear cyclic SEMs with contractive implicit flows whose exogenous noise is Gaussian with a learned covariance; confounders are encoded as noise correlations. Graph structure (Bernoulli adjacency with Gumbel straight-through), network weights and noise covariance are optimized by penalized log-likelihood, using a stochastic unbiased log-determinant estimator and a lasso-based covariance u
Key results
- On Perturb-CITE-seq, DCCD-CONF reports the lowest test NLL in all three conditions (Control 1.375, Co-Culture 1.245, IFN-gamma 1.235), beating NODAGS (1.465/1.406/1.504), LLC and DCDI.
- On synthetic data with d=10, DCCD-CONF achieves lower normalized SHD than baselines across confounder ratios 0.2-0.8 in linear and nonlinear SEMs, and performance gap widens as number of single-node interventions grows.
- Theorem shows that exact maximization of the score recovers the I-Markov equivalence class of the ground-truth directed mixed graph under stated assumptions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DCCD-CONF instead of LLC | Causal discovery on Perturb-CITE-seq · Control test | NLL: 1.385 (0.039) -> 1.375 (0.103) | Helped |
| Use DCCD-CONF instead of LLC | Causal discovery on Perturb-CITE-seq · Co-Culture test | NLL: 1.325 (0.029) -> 1.245 (0.039) | Helped |
| Use DCCD-CONF instead of LLC | Causal discovery on Perturb-CITE-seq · IFN-γ test | NLL: 1.430 (0.048) -> 1.235 (0.338) | Helped |
| Use DCCD-CONF rather than baseline methods for nonlinear SEMs with varying confounder ratios | Synthetic causal graph recovery · Synthetic nonlinear SEMs, confounder ratio 0.2–0.8 | normalized SHD | Helped |
| Increase the number of cycles | DCCD-CONF · Synthetic graphs, d = 10, confounder ratio 0.3 | normalized SHD and confounder F1 | No clear effect |
| Increase nonlinearity in the SEM | DCCD-CONF · Synthetic SEMs, β from 0 to 1 | causal graph and confounder recovery | Helped |
| Use LLC instead of DCCD-CONF in more linear SEMs | Synthetic causal discovery · Synthetic SEMs, small β | causal graph and confounder recovery | Helped |
| Increase the number of training interventions | DCCD-CONF versus baselines · Synthetic nonlinear SEMs, d = 10 | graph recovery performance | Helped |
| Scale the graph to more nodes | DCCD-CONF versus baselines · Synthetic graphs, d from 10 to 80 | normalized SHD and confounder F1 | Mixed |
Surprising findings
- LLC slightly outperforms DCCD-CONF at small nonlinearity (beta near 0), and the two perform comparably around beta=0.25.
- With fewer than about 3 interventions, DCCD-CONF and baselines perform similarly; LLC cannot run in the purely observational setting.
Limitations
- Confounders are restricted to Gaussian exogenous noise; other noise distributions left for future work.
- Requires contractive causal mechanisms, which may be restrictive; the paper notes it may be relaxed only for known acyclic graphs.
- Necessary conditions on interventional targets for perfect recovery in general cyclic DMGs with confounders remain open; guarantees are large-sample.
Experimental setup
Datasets: Perturb-CITE-seq synthetic ER cyclic graphs with Gaussian noise
Benchmarks: Perturb-CITE-seq
Metrics: normalized SHD F1 score on confounder edges negative log-likelihood MAE
Baselines: NODAGS-Flow LLC DAGMA ADMG (linear ADMG recovery) LiNGAM-MMI JCI-FCI DCDFG Bicycle DCDI
Builds on: NODAGS-Flow DAGMA LLC JCI DCDI
Closest papers by meaning
- Stable Differentiable Causal Discovery (ICML 2024 · similarity 0.91)
- THE ROBUSTNESS OF DIFFERENTIABLE CAUSAL DISCOVERY IN MISSPECIFIED SCENARIOS (ICLR 2025 · similarity 0.90)
- Differentiable Causal Discovery for Latent Hierarchical Causal Models (ICLR 2025 · similarity 0.90)
- Interventional Causal Discovery in a Mixture of DAGs (NeurIPS 2024 · similarity 0.89)
- Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency (ICML 2024 · similarity 0.89)
- Coarsening Linear Non-Gaussian Causal Models with Cycles (NeurIPS 2026 · similarity 0.88)
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