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Gradient-Based Neural DAG Learning

ICLR 2020 · Probabilistic and scientific modeling › Causal discovery · approach: Differentiable and score-based DAG learning · 15 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use nonlinear neural conditionals with a continuous acyclicity constraintGraN-DAG versus DAG-GNN · Gauss-ANM, ER1, 10 nodesSHD: 11.4$\pm$3.1 -> 1.7$\pm$2.5Helped
Use nonlinear neural conditionals with a continuous acyclicity constraintGraN-DAG versus DAG-GNN · Gauss-ANM, ER1, 10 nodesSID: 37.6$\pm$14.4 -> 1.7$\pm$3.1Helped
Add PNS and pruning (ablation)GraN-DAG · Gauss-ANM, ER1, 50 nodesSHD: 1086.8$\pm$48.8 -> 6.1$\pm$3.3Helped
Add PNS and pruning (ablation)GraN-DAG · Gauss-ANM, ER1, 50 nodesSID: 31.6$\pm$23.6 -> 29.3$\pm$19.5Mixed
Add PNS without pruning (ablation)GraN-DAG · Gauss-ANM, ER1, 50 nodesSHD: 1086.8$\pm$48.8 -> 540.4$\pm$70.3Helped
Add pruning without PNS (ablation)GraN-DAG · Gauss-ANM, ER1, 50 nodesSHD: 1086.8$\pm$48.8 -> 11.8$\pm$5.0Helped
Allow conditional variance to depend on parent variables (ablation)GraN-DAG (GraN-DAG++) · Protein signaling data setSHD: 13 -> 13No clear effect
Allow conditional variance to depend on parent variables (ablation)GraN-DAG (GraN-DAG++) · SynTReN, 20 nodesSID: 161.7$\pm$53.4 -> 127.5$\pm$52.8Mixed
Use the expected Jacobian rather than weighted adjacency strengths for final edge removal (ablation)GraN-DAG · Structure learning experimentsgraph recoveryHelped
Increase sample size from 500 to 5000 (ablation)GraN-DAG versus CAM · Gauss-ANM, ER4, 50 nodesSID: CAM 845.0 $\pm$ 159.8; GraN-DAG 554.1 $\pm$ 117.9Helped
Apply PNS and pruning to NOTEARS and DAG-GNN (ablation)NOTEARS and DAG-GNN · Gauss-ANM, ER1, 50 nodesSID: DAG-GNN 322.9$\pm$103.8 -> 316.5$\pm$106.9; NOTEARS 327.1$\pm$110.9 -> 326.4$\pm$106.9No clear effect

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