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The computational task of determining the convex hull membership is made feasible even for large numbers of explanatory variables and observations by the solution proposed in King & Zeng (2006), which eliminates the most time-consuming part of the problem: the characterization of the convex hull itself. In addition, they show that the remaining (implicit) point location problem can be expressed as a linear programming exercise, making it possible to take advantage of existing well-developed algorithms designed for other purposes to speed up the computation. Specifically, a counterfactual is in the convex hull of the explanatory variables if there exists a feasible solution to the following standard form linear programming problem:
The default Gower distance (which is suitable for both quantitative and qualitative data) between a pair of dimensional points and is defined simply as the average absolute distance between the elements of the two points divided by the range of the data:
. | (3) |