Causal effect identification considers whether an interventional probability distribution can be uniquely determined from a passively observed distribution in a given causal structure. If the generating system induces context-specific independence (CSI) relations, the existing identification procedures and criteria based on do-calculus are inherently incomplete. We show that deciding causal effect non-identifiability is NP-hard in the presence of CSIs. Motivated by this, we design a calculus and an automated search procedure for identifying causal effects in the presence of CSIs. The approach is provably sound and it includes standard do-calculus as a special case. With the approach we can obtain identifying formulas that were unobtainable previously, and demonstrate that a small number of CSI-relations may be sufficient to turn a previously non-identifiable instance to identifiable.

Drawbacks of ignoring the causal mechanisms when performing imitation learning have recently been acknowledged. Several approaches both to assess the feasibility of imitation and to circumvent causal confounding and causal misspecifications have been proposed in the literature.However, the potential benefits of the incorporation of additional information about the underlying causal structure are left unexplored.An example of such overlooked information is context-specific independence (CSI), i.e., independence that holds only in certain contexts.We consider the problem of causal imitation learning when CSI relations are known.We prove that the decision problem pertaining to the feasibility of imitation in this setting is NP-hard.Further, we provide a necessary graphical criterion for imitation learning under CSI and show that under a structural assumption, this criterion is also sufficient.Finally, we propose a sound algorithmic approach for causal imitation learning which takes both CSI relations and data into account.

This paper proposes an automated search procedure for identifying causal effects when context-specific independence relations are present in an observed distribution. Equipped with sufficient conditions for conditional independence statements (Boutiller et al. 1996) and LDAG representation (Pensar et al. 2015), a simple search algorithm is implemented. Overall, the paper is clearly written, and it was easy to follow theorems (clarity). However, it is hard to measure the novelty of the paper (originality), which I will discuss below. Hence, the proposed algorithm may be useful for some researchers, but its significance (impact) is unclear. It is nice to see the rules (basic probability axioms (CS) independence) written clearly, which lead to the implementation of a search algorithm.

Drawbacks of ignoring the causal mechanisms when performing imitation learning have recently been acknowledged. Several approaches both to assess the feasibility of imitation and to circumvent causal confounding and causal misspecifications have been proposed in the literature.However, the potential benefits of the incorporation of additional information about the underlying causal structure are left unexplored.An example of such overlooked information is context-specific independence (CSI), i.e., independence that holds only in certain contexts.We consider the problem of causal imitation learning when CSI relations are known.We prove that the decision problem pertaining to the feasibility of imitation in this setting is NP-hard.Further, we provide a necessary graphical criterion for imitation learning under CSI and show that under a structural assumption, this criterion is also sufficient.Finally, we propose a sound algorithmic approach for causal imitation learning which takes both CSI relations and data into account.

Causal effect identification considers whether an interventional probability distribution can be uniquely determined from a passively observed distribution in a given causal structure. If the generating system induces context-specific independence (CSI) relations, the existing identification procedures and criteria based on do-calculus are inherently incomplete. We show that deciding causal effect non-identifiability is NP-hard in the presence of CSIs. Motivated by this, we design a calculus and an automated search procedure for identifying causal effects in the presence of CSIs. The approach is provably sound and it includes standard do-calculus as a special case.

Causal effect identification considers whether an interventional probability distribution can be uniquely determined from a passively observed distribution in a given causal structure. If the generating system induces context-specific independence (CSI) relations, the existing identification procedures and criteria based on do-calculus are inherently incomplete. We show that deciding causal effect non-identifiability is NP-hard in the presence of CSIs. Motivated by this, we design a calculus and an automated search procedure for identifying causal effects in the presence of CSIs. The approach is provably sound and it includes standard do-calculus as a special case.