Appraisal theory of emotion claims that emotions are not caused by "raw" stimuli, as such, but by the subjective evaluation (appraisal) of those stimuli. Studies that analyzed this relation have been dominated by linear models of analysis. These methods are not ideally suited to examine a basic assumption of many appraisal theories, which is that appraisal criteria interact to differentiate emotions, and hence show nonlinear effects. Studies that did model interactions were either limited in scope or exclusively theory-driven simulation attempts. In the present study, we improve on these approaches using data-driven methods from the field of machine learning. We modeled a categorical emotion response as a function of 25 appraisal predictors, using a large dataset on recalled emotion experiences (5901 cases). A systematic comparison of machine learning models on these data supported the interactive nature of the appraisal–emotion relationship, with the best nonlinear model significantly outperforming the best linear model. The interaction structure was found to be moderately hierarchical. Strong main effects of intrinsic valence and goal compatibility appraisal differentiated positive from negative emotions, while more specific emotions (e.g., pride, irritation, despair) were differentiated by interactions involving agency appraisal and norm appraisal.