Identification and Estimation under Multiple Versions of Treatment: Mixture-of-Experts Approach

The Stable Unit Treatment Value Assumption (SUTVA) includes the condition that there are no multiple versions of treatment in causal inference. Though we could not control the implementation of treatment in observational studies, multiple versions may exist in the treatment. It has been pointed out that ignoring such multiple versions of treatment can lead to biased estimates of causal effects, but a causal inference framework that explicitly deals with the unbiased identification and estimation has not been fully developed yet. Thus, it is difficult to obtain a deeper understanding for mechanisms of the complex treatments. In this paper, we introduce the Mixture-of-Experts framework into causal inference to estimate causal contrasts between underlying versions of a treatment, even when the versions are not observed. Numerical experiments demonstrate the effectiveness of the proposed method.