Learning Markov Blankets From Multiple Interventional Data Sets.

Learning Markov blankets (MBs) plays an important role in many machine learning tasks, such as causal Bayesian network structure learning, feature selection, and domain adaptation. Since variables included in the MB of a target variable of interest have causal relationships with the target, the MB can serve as the basis of learning the global structure of a causal Bayesian network or as a reliable and robust feature set for classification, both within the same domain or across domains. In this article, we study the problem of learning the MB of a target variable from multiple interventional data sets. Data sets attained from interventional experiments contain richer causal information than passively observed data (observational data) for MB discovery. However, almost all existing MB discovery methods are designed for learning MBs from a single observational data set. To learn MBs from multiple interventional data sets, we face two challenges: 1) unknown intervention variables and 2) nonidentical data distributions. To address these challenges, we theoretically analyze: 1) under what conditions we can find the correct MB of a target variable and 2) under what conditions we can identify the causes of the target variable via discovering its MB. Based on the theoretical analysis, we propose a new algorithm for learning MBs from multiple interventional data sets, and we present the conditions/assumptions that assure the correctness of the algorithm. To the best of our knowledge, this article is the first to present the theoretical analyses about the conditions for MB discovery in multiple interventional data sets and the algorithm to find the MBs in relation to the conditions. Using benchmark Bayesian networks and real-world data sets, the experiments have validated the effectiveness and efficiency of the proposed algorithm in this article.