Google to open artificial intelligence lab in Princeton
princeton.edu
princeton.edu
Google (and microft and...) do support (fund) labs at most of the schools you listed.
Yes, particularly with regards to generalization. There's a large number of theorists racing to explain that.
I wonder how come this is the case from looking at ArXiv, it seems there are plenty of low-hanging fruit relating to the Foundations of Machine Learning.
To speak nothing of the professors...
This probably had a lot to do with it. Schools like that have huge endowments (Princeton's is north of 20 billion dollars), and as such can afford to attract very good faculty. Very good faculty can lead to very bright students.
Princeton is also going to have a lot more defense dealings than something like a state school and where cutting-edge tech is being researched, OGAs are guaranteed to be sniffing around and weaseling their way into the research with funding.
Higher ranked schools are often better at research as well, you can get more bang for your buck than lesser ranked schools.
Note that this depends on what you want for "bang". At less well-heeled schools, a far more modest donation can steer departments etc.
Just to be clear, Princeton ranks close to 15-20th in CS. Many state schools do out rank Princeton in CS and they do not have such labs yet.
I can understand if IAS or the Math department was the main reason to open a lab there. But, if it was quality of CS faculty that exclusively factored into the decision, then there would be other state schools in the line ahead of Princeton.
On the scale of things academics are pretty cheap so they can afford to have lots of offices and cover the top 20 schools. Really they should have one in New Haven as well.
The prestige thing is not as important (I believe). For instance they had offices in Austin and Ann Arbor before Princeton NJ.
The prestige thing is only important for client facing roles (McKinsey or Goldman want to assure the money people that they are in good hands).
But, at the same time, Google already has connections with Princeton, both through these individual profs and through the NY Tech campus (they shared an office with Google before moving to Roosevelt Island).
It is kind of interesting in the trend of professors being more connected with industry and spending time actually working at tech companies. It's both interesting from the perspective of engagement (profs can work on real problems) and frightening from the prospective of independence--the companies will inevitably sway which problems profs work on, and of course their students won't enjoy their advisors' attention being scattered elsewhere.