Obtaining Causal Information by Merging Datasets with MAXENT

The investigation of the question "which treatment has a causal effect on a target variable?" is of particular relevance in a large number of scientific disciplines. This challenging task becomes even more difficult if not all treatment variables were or even cannot be observed jointly with the target variable. Another similarly important and challenging task is to quantify the causal influence of a treatment on a target in the presence of confounders. In this paper, we discuss how causal knowledge can be obtained without having observed all variables jointly, but by merging the statistical information from different datasets. We first show how the maximum entropy principle can be used to identify edges among random variables when assuming causal sufficiency and an extended version of faithfulness. Additionally, we derive bounds on the interventional distribution and the average causal effect of a treatment on a target variable in the presence of confounders. In both cases we assume that only subsets of the variables have been observed jointly.