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Boosting Causal Structure Learning: An Asymmetric Exponential Modulation Gaussian-Based Adaptive Sample Reweighting Framework
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Proposes DAG-AEG, a model-agnostic adaptive sample reweighting framework using an asymmetric exponential modulated Gaussian over per-sample losses to boost differentiable score-based DAG structure learning on synthetic and Sachs data.
Problem
Differentiable score-based causal structure learning uses average scoring that assumes all samples are equally easy and homogeneous, so outliers and heterogeneous data induce spurious edges.
Approach
Reweights samples with an asymmetric exponential modulation of a Gaussian over loss values, suppressing both very easy samples and outliers at the extremes of the loss distribution while upweighting mid-range losses, trained in a bi-level loop with the DAG learner.
Key results
- On ER2 with 10 nodes, NOTEARS+DAG-AEG improves SHD from 5.8 to 2.0 (about 66%) and GOLEM+DAG-AEG reaches TPR 0.95 vs 0.87.
- On Sachs, GraN-DAG+DAG-AEG raises TPR from 0.294 to 0.471 and lowers SID from 60 to 38.
- On synthetic heterogeneous linear data, GOLEM+DAG-AEG improves SHD to 15.1 from 18.7 and outperforms CD-NOD (24.1) and DICD (16.7) on SHD.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply DAG-AEG reweighting to differentiable score-based DAG learners | Linear and nonlinear DAG learners · Synthetic ER graphs | SHD: 3% to 66% over advanced baselines | Helped |
| Apply DAG-AEG reweighting to differentiable score-based DAG learners | Linear and nonlinear DAG learners · Synthetic ER graphs | SID: 7% to 87% over advanced baselines | Mixed |
| Apply DAG-AEG reweighting | GOLEM and NOTEARS-MLP · Synthetic heterogeneous data | TPR: GOLEM: 0.79 -> 0.93; NOTEARS-MLP: 0.62 -> 0.65 | Helped |
| Apply DAG-AEG reweighting | GOLEM and NOTEARS-MLP · Synthetic heterogeneous data | SHD: GOLEM: 18.7 -> 15.1; NOTEARS-MLP: 25.8 -> 22.0 | Helped |
| Apply DAG-AEG reweighting | GraN-DAG · Sachs | TPR: 0.294 -> 0.471 | Helped |
| Apply DAG-AEG reweighting | GraN-DAG · Sachs | SHD: 16 -> 14 | Helped |
| Use fixed IPS sample weights instead of adaptive weights | Baseline DAG learners · Synthetic heterogeneous data | TPR: GOLEM: 0.79 -> 0.65; NOTEARS-MLP: 0.62 -> 0.35 | Hurt |
| Apply ReScore sample reweighting rather than DAG-AEG | DAG learners · Synthetic ER graphs | SHD: DAG-AEG improvement over ReScore: 0 to 40% | Mixed |
| Increase graph size and density | Differentiable score-based baselines · Synthetic ER graphs | TPR | Hurt |
Surprising findings
- Plain IPS reweighting severely reduces TPR on heterogeneous data (e.g., NOTEARS-MLP TPR drops from 0.62 to 0.35 nonlinear), showing fixed weights hurt compared with adaptive weights.
- On dense 50-node graphs, gains are limited and some metrics degrade, e.g., NOTEARS+DAG-AEG SID on 20-node ER4 unchanged or SID slight increases in some settings.
Limitations
- Effectiveness depends on the efficiency of the underlying DAG learner; gains are limited on dense graphs.
- Performance declines sharply as node count grows for dense graphs, with TPR below 50% for nonlinear 50-node settings.
- Bi-level optimization adds training complexity and hyperparameters (beta, gamma, sigma) that are dynamically adjusted without a stated rule.
Experimental setup
Datasets: Synthetic ER graphs (linear and nonlinear) Synthetic heterogeneous data Sachs
Benchmarks: Synthetic ER2/ER4 graphs (d=10,20,50) Synthetic heterogeneous data Sachs
Metrics: TPR FDR SHD SID
Baselines: NOTEARS GOLEM NOTEARS-MLP GraN-DAG ReScore IPS CD-NOD DICD GES
Builds on: NOTEARS ReScore GOLEM GraN-DAG NOTEARS-MLP
Closest papers by meaning
- Boosting Causal Discovery via Adaptive Sample Reweighting (ICLR 2023 · similarity 0.92)
- Pattern-Guided Adaptive Prior for Structure Learning (NeurIPS 2025 · similarity 0.90)
- Effective Causal Discovery under Identifiable Heteroscedastic Noise Model (AAAI 2024 · similarity 0.88)
- Causal Discovery via Bayesian Optimization (ICLR 2025 · similarity 0.88)
- Differentiable Structure Learning with Ancestral Constraints (ICML 2025 · similarity 0.87)
- CoLiDE: Concomitant Linear DAG Estimation (ICLR 2024 · similarity 0.87)
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