Symbolic Computation of Tight Causal Bounds
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Causal inference involves making a set of assumptions about the nature of things, defining a causal query, and attempting to find estimators of the query based on the distribution of observed variables. When causal queries are not identifiable from the observed data, it still may be possible to derive bounds for these quantities in terms of the distribution of observed variables. We develop and describe a general approach for computation of bounds, proving that if the problem can be stated as a linear program, then the true global extrema result in tight bounds. Building upon previous work in this area, we characterize a class of problems that can always be stated as a linear programming problem; we describe a general algorithm for constructing the linear objective and constraints based on the causal model and the causal query of interest. These problems therefore can be solved using a vertex enumeration algorithm. We develop an R package implementing this algorithm with a user friendly graphical interface using directed acyclic graphs, which only allows for problems within this class to be depicted. We have implemented additional features to help with interpreting and applying the bounds that we illustrate in examples.
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