That's not exactly accurate. Ad companies definitely need to train using large data sets, but they could infer with very little information, and in most cases,

That's not exactly accurate. Ad companies definitely need to train using large data sets, but they could infer with very little information, and in most cases, "unstructured" and "low quality" data was actually quite helpful for inferences about a user. Just a free form text box where someone was prompted for "favourite movies" (with no validation of the content... you didn't even have to have any movie titles in it) could yield surprisingly accurate inferences about income, education, gender, religion, age, marital status, etc. Ironically it was more predictive than inferring from structured data.