Everyone knows that story about marketers at Target figuring out that a teenager was pregnant before her parents knew, just based off of her purchases. Does anyone know if there's been research into how well an LLM can predict details about a user? If so, how much does the user have to talk to the LLM, and how much personal info do they have to leak in the conversations, before the predictions become any good?

I can imagine some nightmare scenario where after a few months of me asking occasional technical questions to ChatGPT, OpenAI knows the perfect way to market a new pair of socks to me, or can predict my behavior in some situations before even I know what I would do. It seems weird that there's not more discussion of this online, maybe there really just hasn't been much research?