Most of what I've seen isn't very promising. The energy in these research areas are because it would be so much cheaper than the "right" way, far more than because of the likelihood of success. And also perversely, because it's hard for the academic researchers to get enough data to do other studies :) NB: I'm not saying there is nothing useful coming out of the learning literature in last few years, just that it a) isn't a silver bullet and b) is often being misapplied in these areas anyway.
Label quality and availability isn't the only big problem though. Many data sets exhibit problematic sampling bias, as well as being order(s) of magnitude too small, because of the way they are gathered and how access is granted.