Sure, a simple logistic regression will pick that up. Doesn't mean there is that much thought (rather, 'intelligence') behind it.

Besides, I quite happy (if I have to see ads at all) to not be shown tampons and pokemon cards. I'd much rather see things I might be interested in.

Adsense bidding is going to offer advertisers advertising options based user profiles which are somehow anonymized. So it's not a case of falling into a "cluster": even though I'm a typical male in other respects, the strong correlation of certain pages/searches with particular gender-specific interests swamped everything else and made me apparently attractive to a new set of advertisers.

Any ad for tampons shown to a guy is a waste of space. Its in their interest to classify you by demographic as much as possible. Google has (had?) a page where you can view all your data and they had a list of all your interests (according to your searches presumably).