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Atrial fibrillation (AF) correlates with an increased risk of all-cause mortality or stroke, mainly due to undiagnosed patients and undertreatment. Its screening is thus a key challenge, for which machine learning methods hold the promise of cheaper and faster campaigns. The robustness of such methods to varying artifacts, noise, and conditions is then crucial. We introduce the first distributional support vector machine (SVM) for robust detection of AF from short, noisy electrocardiograms. It achieves state-of-the-art performance and unprecedented robustness on the screening problem while only leveraging one interpretable feature and little training data. We illustrate these advantages by evaluating on other data sources (cross-data-set) and through sensitivity studies. These strengths result from two main components: (i) preliminary peak detection enabling robust computation of medically relevant features; and (ii) a mathematically principled way of aggregating those features to compare their full distributions. This establishes our algorithm as a relevant candidate for screening campaigns.