Optimal estimation of Gaussian DAG models. (arXiv:2201.10548v1 [math.ST])

We study the optimal sample complexity of learning a Gaussian directed
acyclic graph (DAG) from observational data. Our main result establishes the
minimax optimal sample complexity for learning the structure of a linear
Gaussian DAG model with equal variances to be $n\asymp q\log(d/q)$, where $q$
is the maximum number of parents and $d$ is the number of nodes. We further
make comparisons with the classical problem of learning (undirected) Gaussian
graphical models, showing that under the equal variance assumption, these …

arxiv dag math