Differentiable DAG Sampling

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-<PRE_TAG>DP-DAG</POST_TAG>, a new method for DAG learning from observational data which combines DP-DAG with variational inference. Hence,VI-<PRE_TAG>DP-DAG</POST_TAG> approximates the posterior probability over DAG edges given the observed data. VI-<PRE_TAG>DP-DAG</POST_TAG> 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-<PRE_TAG>DP-DAG</POST_TAG> to other differentiable DAG learning baselines on synthetic and real datasets. VI-<PRE_TAG>DP-DAG</POST_TAG> significantly improves DAG structure and causal mechanism learning while training faster than competitors.