Geometric and Quantum Kernel Methods for Predicting Skeletal Muscle Outcomes in chronic obstructive pulmonary disease

arXiv:2601.00921v2 Announce Type: replace Abstract: Quantum methods are increasingly proposed for healthcare, but translational biomarker studies demand transparent benchmarking and robust small-dataset evaluation. We analysed a preclinical COPD cohort of 213 animals with blood and bronchoalveolar-lavage biomarkers to predict tibialis anterior muscle weight, specific force, and muscle quality. We benchmarked tuned classical models against two structured nonlinear low-data strategies: geometry-aware symmetric positive definite (SPD) descriptors, in which training-only clustering maps each subject to Stein-divergence distances from representative prototypes and optional unlabeled synthetic SPD interpolation stabilises prototype discovery; and quantum-kernel regression, including a clustered Nystrom-style feature map that compresses each subject into similarities to a small set of training-derived centres. By replacing full pairwise structure with compact prototype- and centre-based summaries, these steps regularise learning and preserve interpretability in a small-sample setting. Across five outer folds, quantum-kernel ridge regression using four interpretable inputs achieved the best muscle-weight performance (RMSE 4.41 mg; R2 0.62), outperforming a matched compact classical baseline (4.68 mg; R2 0.56). Biomarker-only SPD features also improved over ridge regression (4.55 versus 4.79 mg), and screening evaluation reached ROC-AUC 0.91 for low muscle weight.