Efficient Balanced Treatment Assignments for Experimentation

In this work, we address the problem of balanced treatment assignment for experiments by considering an interpretation of the problem as optimization of a two-sample test between test and control units. Using this lens we provide an assignment algorithm that is optimal with respect to the minimum spanning tree test of Friedman and Rafsky [1979]. This assignment to treatment groups may be performed exactly in polynomial time and allows for the design of experiments explicitly targeting the individual treatment effect. We provide a probabilistic interpretation of this process in terms of the most probable element of designs drawn from a determinantal point process. We provide a novel formulation of estimation as transductive inference and show how the tree structures used in design can also be used in an adjustment estimator. We conclude with a simulation study demonstrating the improved efficacy of our method.