I'm a rising senior majoring in math, and my coursework almost exclusively consists of grad-level pure math courses. However, I'm getting more and more interested in Machine Learning. I've studied applied math and machine learning by myself, and now that I've graduated from a college, I'm going to do research in machine learning full-time with a professor in another institution until the next summer. Nevertheless, I suppose I have better chance for math PhD programs due to my coursework (note that I may not publish before the admission), and there are some non-top-tier (though strong in some areas) math PhD programs whose university has a top-tier group of ML researchers in the CS department. A good example would be CMU. Of course, it would be better if one can go to the universities which are both top-level at math and ML, but math programs of such universities (e.g Berkeley, MIT and Stanford) are harder to get into.
My guess is that I just should go to the math PhD program of CMU if it has a ML researcher of my interest, and everything that decides my career afterward is the quality of my publications. But are there some obvious cons for this option?