Machine learning for an undergrad?

Hey guys! I am an undergrad double majoring in Mathematics and Economics. I have become quite fascinated with Machine Learning over the summer! So I started recently pondering what branches of Mathematics would be a good compliment to Machine Learning. I mean aside from the statistical theory, such as Bayesian statistics, which forms a somewhat of a base for it, what bodies in Mathematics would set the stage for a more complete understanding.

So I thought that a good place to ask this question would be here.

More topology? More combinatorics? More analysis? None of em and something else entirely?

Any comments would be highly appreciated. Thanks!