Latent Dirichlet allocation
Blei, Ng and Jordan described a model that finds hidden topics in a set of documents without being given any labels.
Why it matters
The structure of a large body of text became visible without anyone describing it in advance.
Each document is a mixture of topics and each topic a distribution over words. Inference is approximate because the exact computation is infeasible. The model quickly became standard for exploratory text analysis, then for images, genomics and recommendation. It is one of the few cases where a fully probabilistic model produced a widely used tool.