Complexity, costs, and waiting list issues demand a simplified alternative for sleep apnea-hypopnea syndrome (SAHS) diagnosis. The blood oxygen saturation signal (SpO2) carries useful information about SAHS and can be easily acquired from overnight oximetry. In this study, SpO2 single-channel recordings from 320 subjects were obtained at patients' homes and were used to automatically obtain statistical, spectral, nonlinear, and clinical SAHS-related information. Relevant, nonredundant data from these analyses were subsequently used to train and validate four machine-learning methods with the ability to classify SpO2 signals into one of the four SAHS-severity degrees (no-SAHS, mild, moderate, and severe). All the models trained (linear discriminant analysis, 1-vs-all logistic regression, Bayesian multilayer perceptron, and AdaBoost) outperformed the diagnostic ability of the conventionally used 3% oxygen desaturation index. An AdaBoost model built with linear discriminants as base classifiers reached the highest figures. It achieved 0.479 Cohen's κ in the SAHS severity classification, as well as 92.9%, 87.4%, and 78.7% accuracies in binary classification tasks using increasing severity thresholds (apnea-hypopnea index: 5, 15, and 30 events/hour, respectively). These results suggest that machine-learning can be used along with SpO2 information acquired at a patients' home to help in SAHS diagnosis simplification.