  In this work, we reframe the problem of balanced treatment assignment 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. We provide a
probabilistic interpretation of this process in terms of the most probable
element of designs drawn from a determinantal point process which admits a
probabilistic interpretation of the design. 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.
