A training system is described herein for generating a prediction model that relies on a feature space with reduced dimensionality. The training system performs this task by producing partitions, each of which corresponds to a subset of aspect values (where each aspect value, in turn, may correspond to one or more attribute values). The training system then produces instances of statistical information associated with the partitions. Each instance of statistical information therefore corresponds to feature information that applies to a plurality of aspect values, rather than a single aspect value. The training system then trains the prediction model based on the feature information. Also described herein is a prediction module that uses the prediction model to make predictions in various online contexts.