It depends on what you want to do as a researcher. If you want to prove theorems in machine learning theory, courses like convex optimization make sense. I would also add statistical machine learning (CMU 10-702) for a broader view.

But a large part of ML research is not theoretical stuff, and involves building real systems. And in that case you should get a cursory overview of ML and then focus on the subdomain you may be interested in. By cursory overview I mean getting a gist of things like graphical models, SVMs etc.- a typical entry level grad ML course. This should be enough when you delve deep into your domain of choice.