Robust latent data representations

Economic agents often infer latent structures—such as preference types— from data, without exogenously specified priors. We model such agents as empirical Bayesians. They estimate both the prior over types and the meanings of types via maximum likelihood. We show this estimation is equivalent to decomposing the sample into subsamples, each best explained by a single available latent type, with the decomposition minimizing the average misfit. The equivalence yields structural properties: optimal latent representations are robust (type definitions locally invariant to data changes) and simple (type count bounded). We extend these properties to agents who face frictions in evaluating likelihoods.