Transportability from Multiple Environments with Limited Experiments
This paper considers the problem of transferring experimental findings learned from multiple heterogeneous domains to a target domain, in which only limited experiments can be performed. We reduce questions of transportability from multiple domains and with limited scope to symbolic derivations in the causal calculus, thus extending the original setting of transportability introduced in [1], which assumes only one domain with full experimental information available. We further provide different graphical and algorithmic conditions for computing the transport formula in this setting, that is, a way of fusing the observational and experimental information scattered throughout different domains to synthesize a consistent estimate of the desired effects in the target domain. We also consider the issue of minimizing the variance of the produced estimand in order to increase power.
This paper showed the completeness of do-calculus for 
      nonparametric estimation of a causal effect in a semi-Markovian graph 
      structured causal diagram to which an arbitrary set of interventional and 
      observation distributions conforms. It introduced a problem to infer a 
      causal effect of treatment variables on observables in a target domain by 
      combining data from experiments on simultaneously controllable subsets of 
      variables from multiple domains and formulated it as mz-transportability. 
      It further presented a complete algorithm for determining causal effects. 
      Quality of the paper This paper showed the completeness of 
      do-calculus in a semi-Markovian causal graph in a very generic setting. 
      This consequence clarifies the conditions for the valid causal inference 
      and ensures the validity of the causal inference under the condition. It 
      further formulate a measure named mz-transportability and an algorithm to 
      provide a transport formula for estimating the causal effect. These 
      consequences provides a firm basis of the causal inference. In this 
      regard, the work presented in this paper is highly meaningful. 
      Mathematical formulations and their associated proofs seem to be 
      valid, and thus their technical quality is considered to be high. 
      However, the contents of the paper seem to be too much to fill in the 
      limited length. We could not follow the explanations and the mathematical 
      derivations perfectly since there are some significant explanation gaps 
      because of the limited space for the explanation. For example, at the 
      beginning of the subsection 4.1, the authors claim that "We use the 
      notational conventions and definitions for causal models introduced in [2, 
      15, 12]." In this sense, this paper is not self-contained. In addition, in 
      the latter half of the subsection 4.2, the authors missed to explain the 
      definition of "c-componets". Moreover, the entire description of the paper 
      lacks the explanation through some comprehensible examples. The use of the 
      examples eases a lot the comprehension of the readers particularly in this 
      type of theoretical papers. Though these are issues of the paper 
      presentation, this affect the value of the paper. Clarity The 
      explanation and the proofs provided in the paper seems mathematically 
      rigorous. However, as pointed out above, the contents of the paper is too 
      much for the NIPS page limitation. The characterization of the 
      mz-transportation can be far more reduced to provide some basis only for 
      the algorithm in the subsection 4.3. The characterization can be presented 
      in its journal paper version. By presenting the essential skeleton of the 
      contents, the authors can show sufficient value of this study. 
      Originality The mathematical and technical quality of this 
      paper seems high. However, the scope of the paper is rather incremental, 
      and it does not provide entirely novel principles in this research field. 
      Significance The consequence of this paper widely enables 
      causal analysis over multiple domains while ensuring the identifiability 
      of the causal structures. The paper is significant in this regard. But, 
      the paper does not include any experimental validation of the proposed 
      consequences. If some numerical experiments applying the proposed 
      algorithms were demonstrated, the significance of the result could be more 
      clearly indicated.