Voronoi-Calibrated Order Selection for Bayesian Softmax-Gated Mixtures of Experts

Bayesian softmax-gated Gaussian mixture-of-experts (SMoGE) models provide a flexible framework for modelling heterogeneous relationships between covariates and multivariate responses. A key challenge is selecting the number of experts, $K^\star$. We propose V-MTM, a Voronoi-calibrated Merge-Truncate-Merge post-processor, which starts from an overspecified softmax-gated Gaussian MoE and exploits a novel Voronoi loss tailored to SMoGE to recover the $K^\star$. Unlike standard Bayesian model-selection approaches that fit and compare models with different numbers of experts, our methods leverage the geometric contraction of an overspecified posterior towards the true model. We establish a theoretical order-recovery guarantee for V-MTM. Simulation studies demonstrate reliable recovery of $K^\star$ and competitive performance against Bayesian model-selection baselines. On a rice genomic-prediction task, V-MTM returns a posterior over the number of experts that recovers biologically meaningful subpopulation regimes, validated by held-out prediction, which standard selectors miss.