  New biological assays like Perturb-seq link highly parallel CRISPR
interventions to a high-dimensional transcriptomic readout, providing insight
into gene regulatory networks. Causal gene regulatory networks can be
represented by directed acyclic graph (DAGs), but learning DAGs from
observational data is complicated by lack of identifiability and a
combinatorial solution space. Score-based structure learning improves practical
scalability of inferring DAGs. Previous score-based methods are sensitive to
error variance structure; on the other hand, estimation of error variance is
difficult without prior knowledge of structure. Accordingly, we present
$\texttt{dotears}$ [doo-tairs], a continuous optimization framework which
leverages observational and interventional data to infer a single causal
structure, assuming a linear Structural Equation Model (SEM).
$\texttt{dotears}$ exploits structural consequences of hard interventions to
give a marginal estimate of exogenous error structure, bypassing the circular
estimation problem. We show that $\texttt{dotears}$ is a provably consistent
estimator of the true DAG under mild assumptions. $\texttt{dotears}$
outperforms other methods in varied simulations, and in real data infers edges
that validate with higher precision and recall than state-of-the-art methods
through differential expression tests and high-confidence protein-protein
interactions.
