Discovering rare cancer driver genes is difficult because their mutational frequency is too low for statistical detection by computational methods. EPIMUTESTR is an integrative nearest-neighbor machine learning algorithm that identifies such marginal genes by modeling the fitness of their mutations with the phylogenetic Evolutionary Action (EA) score. Over cohorts of sequenced patients from The Cancer Genome Atlas representing 33 tumor types, EPIMUTESTR detected 214 previously inferred cancer driver genes and 137 new candidates never identified computationally before of which seven genes are supported in the COSMIC Cancer Gene Census. EPIMUTESTR achieved better robustness and specificity than existing methods in a number of benchmark methods and datasets.