below). Using the related literature on active interventions would require full identification of the underlying DAG. It is emphasized that matching only the means can be done with significantly smaller number of interventions, and this is the difference from previous works. - Identifiability in terms of Markov equivalence classes (MEC) is well discussed. Graphical characterization of the proposed shift-interventional (shift-I) MEC, and its refinement over the general interventional MEC is given clearly. Assumptions are reasonable within the given setting. - Extending the decomposition of intervention essential graphs to shift interventional essential graphs is sound. Both of the proposed approaches for solving the problem, clique tree and supermodular strategies are reasonable. Use of a lower bound surrogate function to enable supermodularity is clever. - The paper is organized clearly, and the theoretical claims are well supported.
Weaknesses: I have several concerns on the importance of the proposed settings and usefulness of the results. - Although the causal matching problem seems interesting and new, it is not well motivated. To the reviewer’s knowledge, interventions on a causal model are tied to inferring the underlying structure (it does not need to be the whole structure of the model). In this regard, it is not clear how exactly matching the means of a causal system is preferable to performing more relaxed cases of soft interventions. The authors are encouraged to further explain how this setting can be beneficial. - Deterministic shift interventions are useful to test the applicability of the proposed ideas. However, restricting the problem setting to only shift interventions is quite limited and leads to some rather trivial results. For instance, existence and uniqueness results of matching shift-intervention in Lemma 1, and the properties of source nodes in Lemma 2 are immediate observations in a DAG. - Clique tree approximation is just a minor modification of the cited central node algorithm (Greenewald et al., 2019). - Complexity of the submodularity approach subroutine uses SATURATE algorithm (Krause et al., 2008), and is said to scale with N 5
in appendix D.4. It is worth commenting on the feasibility of this approach. For instance, what are the runtimes of the simulations for large models in Section 6? - It is a nice result that the number of proposed interventions is only a logarithmic factor of the lower bound. However, the baselines in the simulations are not very strong to demonstrate the usefulness. Though coloring approach of Shanmugam et al., 2015 is a related active intervention design, the goal of it is broader than finding a matching intervention. For instance, a simple random upstream search, the other baseline, performs much better than coloring due to the simpler objective. That being said, the reviewer understands that the proposed task is new and fair comparisons may not be easy.
Although this paper has several nice properties, the overall contribution, constraints on the problem, and the importance of the results are not adequate for publication at NeurIPS.
Main limitations of the work, which are also stated in the above review, and potential impact of the work, which is not very imminent, are adequately addressed in the discussion section.
- Although the causal matching problem seems interesting and new, it is not well motivated. To the reviewer’s knowledge, interventions on a causal model are tied to inferring the underlying structure (it does not need to be the whole structure of the model). In this regard, it is not clear how exactly matching the means of a causal system is preferable to performing more relaxed cases of soft interventions. The authors are encouraged to further explain how this setting can be beneficial.