Is it possible to achieve greater than perfect compression using machine learning and big data?
Is it possible to achieve greater than perfect compression...


No.  Any lossless compression scheme that makes at least one string shorter must make at least one string longer. This is an unavoidable consequence of the simple fact that there are more long strings than short ones.

The best you can do is be smart about what strings get made shorter, and I guess that's what you're trying to do with machine learning, big data, and any other applicable buzzwordstechnologies. Effectively, though, you're trying to use a big global dictionary.  This is probably less efficient than standard dictionary compression which builds up the dictionary from the data that's being compressed (a dictionary containing lots of Spanish and Chinese isn't going to be useful for compressing Stack Exchange, for example). Also, if you're going to cut network traffic, that big global dictionary needs to be already sitting on your computer, taking up huge amounts of space for dictionary entries you'll probably never use.
Indeed, if that huge dictionary comes as part of my next Chrome update, it's not even obvious that there'll be a net saving in data transfer.