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Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models
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Proposes a hybrid global causal discovery approach combining a top-down hierarchical topological sort (LHTS for linear non-Gaussian ANMs, NHTS for nonlinear ANMs) with a nonparametric constraint-based edge discovery algorithm (ED) that conditions on local sets.
Problem
Global causal discovery of a unique DAG from observational data under additive noise models is either computationally infeasible (curse of dimensionality in high-dimensional nonparametric regression) or relies on strong parametric assumptions, and existing methods scale poorly on sparse graphs.
Approach
Exploit local causal substructures: use ancestral relations (linear) or parent-child relations via active causal paths (nonlinear) to build a hierarchical top-down ordering from roots, then prune edges using nonparametric conditional independence tests conditioned on small local sets (confounders of parent and mediators between the pair).
Key results
- LHTS yields orderings with roughly 70% fewer layers than DirectLiNGAM, though its A_top is consistently lower than DirectLiNGAM's in the reported experiments.
- NHTS achieves the highest median A_top across all trials among baselines including GES, GRaSP, GSP, DirectLiNGAM, NoGAM, and R^2-Sort, and runs up to 4x faster than NoGAM.
- ED achieves the highest median F1 in all trials against CAM-pruning, Lasso, and RESIT when given correct topological orderings.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LHTS instead of DirectLiNGAM | Linear topological sorting · Synthetic linear ANMs | A_top | Hurt |
| Use LHTS instead of R²-Sort | Linear topological sorting · Synthetic linear ANMs | A_top | Helped |
| Use LHTS instead of DirectLiNGAM | Linear topological sorting · Synthetic linear ANMs | number of layers: roughly ∼70% fewer layers | Helped |
| Use NHTS instead of the evaluated baselines | Nonlinear topological sorting · Synthetic nonlinear ANMs | A_top | Helped |
| Use NHTS instead of NoGAM | Nonlinear topological sorting · Synthetic nonlinear ANMs | runtime: up to 4× faster | Helped |
| Use ED instead of the evaluated edge-pruning baselines | Edge pruning with correct topological sorts · Synthetic nonlinear DGPs, uniform noise | F_1 | Helped |
| Use ED instead of Lasso regression | Edge pruning with correct topological sorts · Synthetic nonlinear DGPs, uniform noise | runtime | Hurt |
| Use ED instead of CAM-pruning or RESIT | Edge pruning with correct topological sorts · Synthetic nonlinear DGPs, uniform noise | runtime | Helped |
Surprising findings
- LHTS has consistently lower A_top than DirectLiNGAM despite encoding more causal information in fewer layers.
Limitations
- Full ANM setting (mixed linear and nonlinear functions) not handled; future work.
- Assumes causal sufficiency (no unmeasured confounding) and identifiability conditions.
- Evaluation limited to synthetic data generated with reduced R^2-sortability.
Experimental setup
Datasets: synthetic Erdos-Renyi DAGs with linear, quadratic mechanisms and Gaussian, Uniform, Laplace noise
Benchmarks: synthetic DAGs
Metrics: A_top (percentage of edges recovered by topological ordering F1
Baselines: DirectLiNGAM R^2-Sort GES GRaSP GSP NoGAM CAM-pruning Lasso RESIT
Builds on: DirectLiNGAM RESIT NoGAM CAM-pruning
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