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Title: Bayes optimal estimator of the mean intervention effect and its approximation based on variational inference Authors:  Shunsuke Horii - Waseda University (Japan) [presenting]
Abstract: To estimate the causal effect under Structural Causal Models (SCMs), it has to know or estimate the model that generates the data. However, it is often difficult or impossible to verify which model is correct based only on the data, so some models remain as candidates for the data generating model. We first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating the causal effect under a fixed single model. This idea is also known as Bayesian model averaging, and we attempt to apply it to the causal estimation under SCM. Although the Bayesian model averaging is optimal, as the number of candidate models increases, the weighting calculations become computationally hard. We develop an approximation to the Bayes optimal estimator by using the variational Bayes method. We show the effectiveness of the proposed methods through numerical experiments based on synthetic and semi-synthetic data.