Efficient Balanced Treatment Assignments for Experimentation
This work addresses the challenge of designing efficient experiments for researchers in fields like statistics and causal inference, though it appears incremental as it builds on existing test methods.
The paper tackles the problem of balanced treatment assignment by reframing it as optimizing a two-sample test, resulting in an algorithm that can be performed exactly in polynomial time and showing improved efficacy in simulations.
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.