Human breath contains hundreds of volatile molecules that can provide powerful, non-intrusive spectral diagnosis of a diverse set of diseases and physiological/metabolic states. To unleash this tremendous potential for medical science, we present a robust analytical method that simultaneously measures tens of thousands of spectral features in each breath sample, followed by efficient and detail-specific multivariate data analysis for unambiguous binary medical response classification. We combine mid-infrared cavity-enhanced direct frequency comb spectroscopy (CE-DFCS), capable of real-time collection of tens of thousands of distinct molecular features at parts-per-trillion sensitivity, with supervised machine learning, capable of analysis and verification of extremely high-dimensional input data channels. Here, we present the first application