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If I have an MSc degree in mathematics specializing in machine learning, is it possible to enter a PhD program in computer science (also specializing in machine learning)? Will the fact that my degree is in mathematics and not computer science prevent me from doing that? I have heard of people (in my city, a few years ago) who did a degree in mathematics and then did a graduate degree in a different field (like electrical engineering with cryptography focus or economics, without any degree in that other field), so this seems to be possible. How easy/difficult would it be to get into the CS PhD program (considering my area of specialty is the same)?

In addition, what are the differences in employability for a computer science PhD and a mathematics PhD, with both of them being in machine learning? Is one degree or the other preferred by different sectors?