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Starting with the work of Jaakkola and Haussler, a variety of approaches have been proposed for coupling domain-specific generative models with statistical learning methods. The link is established by a kernel function which provides a similarity measure based inherently on the underlying model. In computational biology, the full promise of this framework has rarely ever been exploited, as most kernels are derived from very generic models, such as sequence profiles or hidden Markov models. Here, we introduce the MTreeMix kernel, which is based on a generative model tailored to the underlying biological mechanism. Specifically, the kernel quantifies the similarity of evolutionary escape from antiviral drug pressure between two viral sequence samples. We compare this novel kernel to a standard, evolution-agnostic amino acid encoding in the prediction of HIV drug resistance from genotype, using support vector regression. The results show significant improvements in predictive performance across 17 anti-HIV drugs. Thus, in our study, the generative-discriminative paradigm is key to bridging the gap between population genetic modeling and clinical decision making.