Regularized Estimation and Feature Selection in Mixtures of Generalized Linear Experts
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The paper investigates how multiple optimal heads in federated averaging affect the global model in multivariate regression with private backbones and a shared linear head. By introducing a natural selection rule—each client returns the head closest to the broadcast head—and analyzing an unconstrained feature model, the authors show that the shared Gram matrix converges to the Bures‑Wasserstein barycenter of the clients’ optimal Gram matrices, which generally differs from the centralized optimum. A one‑time exchange of target means and covariances can correct this gap, restoring the centralized optimal Gram matrix in a single round under exact local optimization.
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.
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