What level of math is required for machine learning research
There can be no objective answer to this question. Obviously the more one understands the better, but the field of ML is vast, quite specialized and ranges from very theoretical to very applied research, so it's perfectly reasonable to publish in ML without a strong background in maths. 

A better way to estimate your own ability to publish papers in a particular area or journal is to study recent papers published in this area/journal. You should be able not only to understand them but to redo the reasoning: 


Understand the problem and the solution proposed by the authors
starting from the initial problem, how would you solve it? Can you think of alternatives to the authors' solution? 
Can you find limitations to their approach and improve on it?


If you reach step 3 then congratulations: you are ready to publish your own research!