Visualization recommender systems aim to lower the barrier to exploring basic visualizations by automatically generating results for analysts to search and select, rather than manually specify. Here, we demonstrate a novel machine learning-based approach to visualization recommendation that learns visualization design choices from a large corpus of datasets and associated visualizations. First, we identify five key design choices made by analysts while creating visualizations, such as selecting a visualization type and choosing to encode a column along the X- or Y-axis. We train models to predict these design choices using one million dataset-visualization pairs collected from a popular online visualization platform. Neural networks predict these design choices with high accuracy compared to baseline models. We report and interpret feature importances from one of these baseline models. To evaluate the generalizability and uncertainty of our approach, we benchmark with a crowdsourced test set, and show that the performance of our model is comparable to human performance when predicting consensus visualization type, and exceeds that of other visualization recommender systems.