Differentiable DAG Sampling

About

We propose a new differentiable probabilistic model over DAGs (DP-DAG). DP-DAG allows fast and differentiable DAG sampling suited to continuous optimization. To this end, DP-DAG samples a DAG by successively (1) sampling a linear ordering of the node and (2) sampling edges consistent with the sampled linear ordering. We further propose VI-DP-DAG, a new method for DAG learning from observational data which combines DP-DAG with variational inference. Hence,VI-DP-DAG approximates the posterior probability over DAG edges given the observed data. VI-DP-DAG is guaranteed to output a valid DAG at any time during training and does not require any complex augmented Lagrangian optimization scheme in contrast to existing differentiable DAG learning approaches. In our extensive experiments, we compare VI-DP-DAG to other differentiable DAG learning baselines on synthetic and real datasets. VI-DP-DAG significantly improves DAG structure and causal mechanism learning while training faster than competitors.

Bertrand Charpentier, Simon Kibler, Stephan Günnemann · 2022

Related benchmarks

Task	Dataset	Result
DAG Structure Recovery	non-linear-1 5000 samples	SHD3.1	48
Causal Discovery	Sachs real-world data protein signaling network	SHD42.6	41
Causal Discovery	Syntren	F1 Score6.9	22
Causal Discovery	Sachs real data d=11	SHD—	19
Causal Discovery	non-linear-2 d=10, 5000 samples (test)	SHD2.8	12
Causal Discovery	non-linear-2 (d=20, 5000 samples) (test)	SHD9.3	12
Causal Structure Learning	Linear Synthetic Data d=10 5000 samples	SHD2.1	12
Causal Structure Learning	Linear Synthetic Data d=20, 5000 samples	SHD4.5	12
Causal Discovery	non-linear-2 d=50, 5000 samples (test)	Structural Hamming Distance23.8	12
Causal Discovery	non-linear-2 d=100, 5000 samples (test)	Structural Hamming Distance (SHD)67.3	12