Model-Agnostic Decomposition of the Difference in Mean Response Between Two Groups via Game-Theoretic Attribution with Minimum-Switching-Distortion Coupling

Model-agnostic decomposition (MAD) with minimum-switching-distortion (MSD) coupling splits the UK–US mean BMI gap for males aged 30–70 into aggregate structure and composition effects plus genus-level allocations.

• Why it matters: Group mean differences can reflect either how covariates relate to response or how covariates are distributed, but separating these contributions is hard without assuming a specific model form.
• What they did: MAD uses an Owen value from a cooperative switching game to derive structure and composition, then allocates composition across covariates using an internal game; MSD coupling is an optimal-transport solution that resolves hybrid-covariate indeterminacy.
• The result: Simulations show MAD and MSD improve decomposition accuracy while meeting coupling admissibility and keeping computational cost manageable, and the UK–US BMI example enables aggregate and microbial-genus-level attribution.

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