Your Math and Stats background is really good for Machine Learning, so that is a positive. Your case reminds me of Christopher Scaffidi - he had a background in Physics (I believe he had a MS in Physics) before he decided he wanted a PhD in Computer Science. He did the CS GRE and scored very highly on it and got into Carnegie Mellon and he's now a prof at Oregon State. So you could consider doing the CS GRE since it tests a wide background of undergraduate CS knowledge. That test is pretty hard though and will require hundreds of hours of preparation for someone without a CS background, but doing well on it would show your competence of undergraduate CS topics.
Alternatively, you could consider some mathematically slanted computer science programs. I'm thinking specifically of the University of Alberta, that has a very good machine learning group. They have a Statistical Machine Learning program that is geared towards people with either a Maths background or a CS background, so you can look into that. I'm sure there are other similar programs out there as well. Best of luck!