SoftBlock: Efficient and Optimal Treatment Assignment for Experiments

• Activity Number: 204 - Experimental Design
• Type: Contributed
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Peter Dimmery* and David Arbour and Anup Rao
• Companies: Facebook and Adobe Research and Adobe Research
• Keywords: experimental design; causal inference; transductive inference; determinantal point processes; two-sample testing

Abstract

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 rapidly mixing Metropolis-Hastings scheme. 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. A standard sandwich estimator provides conservative variance estimation. We conclude with a simulation study demonstrating the improved efficacy of our method.