- Open Access
Model-based equitable learning framework for high-dimensional biomedical data
APS Open Sci. 1, 000084 – Published 5 August, 2026
DOI: https://doi.org/10.1103/dgj9-5fck
Abstract
High-dimensional biomedical studies routinely confront three coupled obstacles: structured population heterogeneity, latent technical confounding, and representational inequity that can degrade inference for under-represented groups. We develop the model-based equitable learning framework (M-ELF), a probabilistic inference architecture that unifies (1) a hierarchical mixture of factor analyzers for subgroup-aware latent structure learning, (2) a negative-control-informed adjustment that removes latent confounding through a partitioned Gaussian conditioning argument, and (3) a spectral-entropy equity regularizer that discourages representation collapse within minority subpopulations using a normalized Vendi score. The M-ELF formulation makes explicit the assumptions required for valid deconfounding and for cross-population comparability of latent factors. The model yields a scalable variational-EM procedure that couples conjugate mixture-factor updates with differentiable spectral regularization. We establish conditions for generic identifiability (up to standard mixture label switching and random-effect rotations), derive exact confounder-elimination statements for the conditional model, and provide an ascent and stationarity analysis for the regularized algorithm. Simulations and a real breast-cancer gene-expression application illustrate that, relative to unadjusted analysis, M-ELF attenuates associations with technical confounders by up to while preserving factor recovery under equity regularization. In the TCGA breast-cancer data, M-ELF attained higher PAM50 subtype agreement (adjusted Rand index) and lower batch association than the specialized deconfounders RUV-2 and PEER, with the equity weight mildly trading off subtype agreement against representation balance. In the model-based simulations, specialized methods can achieve higher factor recovery on individual metrics, and the equity penalty produces only modest changes in cross-population diversity. M-ELF's advantage is the unified probabilistic treatment of subgroup structure, negative-control deconfounding, and equity-aware representation, and should be selected against the scientific end point.
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