“…I n many settings , researchers seek to measure differences in the choices made by different groups, and the way such differences evolve over time. Examples include measuring the extent of racial segregation in residential choices (Reardon and Firebaugh ()), of partisanship in digital media consumption (Gentzkow and Shapiro (), Flaxman, Goel, and Rao ()), of geographic differences in treatment choices of physicians (Chandra, Cutler, and Song ()), and of differences between demographic groups in survey responses (Bertrand and Kamenica ()). We consider the problem of measuring such differences in settings where the dimensionality of the choice set is large—that is, where the number of possible choices is large relative to the number of actual choices observed.…”