Abstract:
We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) G∗ while minimizing the number of interventions made. In our setting, we are additionally given side information about G∗ as advice, e.g. a DAG G purported to be G∗. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on _algorithms with predictions_. When the advice is a DAG G, we design an adaptive search algorithm to recover G∗ whose intervention cost is at most O(max{1,logψ}) times the cost for verifying G∗; here, ψ is a distance measure between G and G∗ that is upper bounded by the number of variables n, and is exactly 0 when G=G∗. Our approximation factor matches the state-of-the-art for the advice-less setting.
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