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Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithm

ICLR 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Interventional causal discovery · 0 citations (OpenAlex)

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Proposes Intersort, a score-based method that orders variables causally from single-variable interventional datasets using a marginal-distribution-based epsilon-interventional faithfulness assumption, with theoretical error bounds.

Problem

Recovering causal order (topological order) from large numbers of single-variable interventions, where existing causal discovery methods perform poorly and rely on strong assumptions.

Approach

Introduces epsilon-interventional faithfulness (marginal distribution shifts under interventions above a threshold indicate directed paths) and a score on causal orders built from Wasserstein distances between observational and interventional marginals; proves optimum recovers the causal order under full intervention and bounds expected error under random intervention.

Key results

• Intersort outperforms PC, GIES, DCDI and EASE on almost all simulated settings with 30 variables, with only GIES (linear) and DCDI (NN, 25-50% intervened) performing better.
• Theory: with all variables intervened, the optimal permutation has D_top = 0; with uniform random intervention probability p, expected D_top is bounded by a quantity that is O(d).
• Intersort's local search result is close to the exact optimum on 5-variable graphs, with overlapping 95% confidence intervals.

Measured effects reported in the paper

Surprising findings

• Standardizing data removes varsortability, and Intersort is robust to normalization, a failure mode of many continuous-optimization methods.

Limitations

• Theoretical guarantees assume epsilon-interventional faithfulness, which is unverifiable in practice and only partially characterized.
• Local search may become computationally expensive for large d; error exceeds upper bounds in many large-scale settings.
• Epsilon must be chosen manually (e.g., 0.3, 0.5), and the bounds assume uniform random intervention selection.

Experimental setup

Datasets: simulated linear data random Fourier features data neural network data SERGIO single-cell simulated data flow cytometry dataset (qualitative)

Benchmarks: simulated linear, RFF, NN and SERGIO GRN data with 10, 30, 100 variables flow cytometry (Sachs) qualitative example

Metrics: D_top (top order divergence) normalized expected error

Baselines: PC GIES DCDI EASE

Builds on: faithfulness top order divergence EASE GES

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