First of all congratulations on your achievements. I am going through a course on Data Analytics in my university (masters course) so I keep coming across problems
like gender classification etc, i.e. the practical problems i.e. finding out from user behaviour what is classification of users so that targeted ads can be served to users.
https://www.techgig.com/hackathon/colombiaonline
That was just a kind of problem I mentioned which might be some thing similar to what you are looking for.
There are many more similar to this.
Can you for the post your GRE scores,your profile etc so that it can help people who are aiming for a PhD
in the universities you mentioned.