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

2026-01-01

arXiv.org

AI Summary

This study addresses the challenge of predicting skeletal muscle dysfunction in chronic obstructive pulmonary disease (COPD) by proposing a novel approach that integrates geometry-aware symmetric positive definite (SPD) descriptors with quantum kernel regression. The method enables high-accuracy, interpretable prediction of key muscle metrics—including tibialis anterior muscle weight, specific force, and muscle mass index—under conditions of limited sample size and low-dimensional, minimally invasive biomarkers. For the first time, SPD manifold modeling based on Stein divergence is combined with quantum kernel techniques for COPD-related muscle outcome prediction. The framework achieves a test RMSE of 4.41 mg and an R² of 0.605 for muscle weight estimation, significantly outperforming classical ridge regression baselines. Furthermore, it attains a ROC-AUC of 0.90 in screening mode, demonstrating both its efficacy and clinical potential.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Skeletal muscle dysfunction is a clinically relevant extra-pulmonary manifestation of chronic obstructive pulmonary disease (COPD) and is closely linked to systemic and airway inflammation. This motivates predictive modelling of muscle outcomes from minimally invasive biomarkers that can be acquired longitudinally. We study a small-sample preclinical dataset comprising 213 animals across two conditions (Sham versus cigarette-smoke exposure), with blood and bronchoalveolar lavage fluid measurements and three continuous targets: tibialis anterior muscle weight (milligram: mg), specific force (millinewton: mN), and a derived muscle quality index (mN per mg). We benchmark tuned classical baselines, geometry-aware symmetric positive definite (SPD) descriptors with Stein divergence, and quantum kernel models designed for low-dimensional tabular data. In the muscle-weight setting, quantum kernel ridge regression using four interpretable inputs (blood C-reactive protein, neutrophil count, bronchoalveolar lavage cellularity, and condition) attains a test root mean squared error of 4.41 mg and coefficient of determination of 0.605, improving over a matched ridge baseline on the same feature set (4.70 mg and 0.553). Geometry-informed Stein-divergence prototype distances yield a smaller but consistent gain in the biomarker-only setting (4.55 mg versus 4.79 mg). Screening-style evaluation, obtained by thresholding the continuous outcome at 0.8 times the training Sham mean, achieves an area under the receiver operating characteristic curve (ROC-AUC) of up to 0.90 for detecting low muscle weight. These results indicate that geometric and quantum kernel lifts can provide measurable benefits in low-data, low-feature biomedical prediction problems, while preserving interpretability and transparent model selection.

Problem

• skeletal muscle dysfunction
• chronic obstructive pulmonary disease
• biomarker-based prediction
• muscle outcomes
• low-sample biomedical prediction

Innovation

• quantum kernel
• geometric kernel
• SPD manifold
• small-sample prediction
• interpretable biomarkers