The outcomes of elections, product sales, and the structure of social connections are all determined by the choices individuals make when presented with a set of options, so understanding the factors that contribute to choice is crucial. Of particular interest are context effects, which occur when the set of available options influences a chooser's relative preferences, as they violate traditional rationality assumptions yet are widespread in practice. However, identifying these effects from observed choices is challenging, often requiring foreknowledge of the effect to be measured. In contrast, we provide a method for the automatic discovery of a broad class of context effects from observed choice data. Our models are easier to train and more flexible than existing models and also yield intuitive, interpretable, and statistically testable context effects. Using our models, we identify new context effects in widely used choice datasets and provide the first analysis of choice set context effects in social network growth.