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Discovering cause-effect relationships between variables from observationaldata is a fundamental challenge in many scientific disciplines. However, inmany situations it is desirable to directly estimate the change in causalrelationships across two different conditions, e.g., estimating the change ingenetic expression across healthy and diseased subjects can help isolategenetic factors behind the disease. This paper focuses on the problem ofdirectly estimating the structural difference between two structural equationmodels (SEMs), having the same topological ordering, given two sets of samplesdrawn from the individual SEMs. We present an principled algorithm that canrecover the difference SEM in $\mathcal{O}(d^2 \log p)$ samples, where $d$ isrelated to the number of edges in the difference SEM of $p$ nodes. We alsostudy the fundamental limits and show that any method requires at least$\Omega(d' \log \frac{p}{d'})$ samples to learn difference SEMs with at most$d'$ parents per node. Finally, we validate our theoretical results withsynthetic experiments and show that our method outperforms thestate-of-the-art. Moreover, we show the usefulness of our method by using datafrom the medical domain.

Direct Learning with Guarantees of the Difference DAG Between Structural Equation Models