MOTIVATION: Machine learning analyses of molecular omics datasets largely drive the development of precision medicine in oncology, but mathematical challenges still hamper their application in the clinic. In particular, omics-based learning relies on high dimensional data with high degrees of freedom and multicollinearity issues, requiring more tailored algorithms. Here, we have developed a prediction algorithm that relies on the 1-Wasserstein distance to better capture complex relationships between variables, and that is built on a decision rule based on the exact computation of the Kantorovich-Rubinstein optimizer to increase the algorithm precision. We explored dimension reduction and aggregation methods to improve its robustness. The exact method was compared with a neural network-based approximate method, as well as with standard Euclidean distance-based classifiers. RESULTS: Experimental results on synthetic datasets with multiple scenarios of redundant/informative variables revealed that exact and approximate methods based on Wasserstein distance outperformed state-of-the-art algorithms when class information was spread across a large number of variables. When predicting clinical or biological outcomes from transcriptomics datasets, HABiC achieved consistently higher accuracy in most situations. AVAILABILITY AND IMPLEMENTATION: Python code for the HABiC classifier is available at https://github.com/chiaraco/HABiC.