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In many real-world scenarios, such as gene knockout experiments, targetedinterventions are often accompanied by unknown interventions at off-targetsites. Moreover, different units can get randomly exposed to different unknowninterventions, thereby creating a mixture of interventions. Identifyingdifferent components of this mixture can be very valuable in some applications.Motivated by such situations, in this work, we study the problem of identifyingall components present in a mixture of interventions on a given causal BayesianNetwork. We construct an example to show that, in general, the components arenot identifiable from the mixture distribution. Next, assuming that the givennetwork satisfies a positivity condition, we show that, if the set of mixturecomponents satisfy a mild exclusion assumption, then they can be uniquelyidentified. Our proof gives an efficient algorithm to recover these targetsfrom the exponentially large search space of possible targets. In the morerealistic scenario, where distributions are given via finitely many samples, weconduct a simulation study to analyze the performance of an algorithm derivedfrom our identifiability proof.

Disentangling Mixtures of Unknown Causal Interventions