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Conditional on someone already knowing they want to do a PhD in machine learning, what are the best two majors that this student could choose for their undergraduate education? Or, what combination of minors and majors is the best? I am mostly interested in developing new algorithms, improving existing algorithms, and applying them to a wide variety of ML problems, instead of narrowly specialising in one area (e.g. computer vision) for my whole career. I've narrowed it down to three majors, and need advice on which two of the three to pick (or which combination of minors/majors): The problem with excluding Statistics from the choice would be no comprehensive formal education in Bayesian statistics, mathematical statistics, and statistical decision theory in general. Traditional classifiers and OLS/GLM would be covered in a CS faculty intro to ML course so I am not worried about those. The problem with excluding Mathematics would be shaky foundations in real analysis, limited to no measure theory, perhaps no multivariate calculus (linear algebra should be covered sufficiently in a Statistics & Computer Science double major), no topology (think manifold learning). The problem with excluding computer science would be no undergraduate AI/ML courses, algorithms/data structures, and theoretical computer science courses, as well as other computer science knowledge that would be generally expected of a graduate student in a CS faculty. Note that I'm already good at programming in multiple languages so this isn't a concern when it comes to the possibility of not doing a CS major (although my lack of knowledge of how computers work could be a problem if I need to use CUDA to do deep learning with 50 GPUs for instance). |
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I think you should add physics. Lots of ML people have a background in physics and the tools you learn during your studies seem to be very close to what you need when you apply ML. Anyway, it depends very much on your curriculum. You can do a major in each and will be able to do a Phd in machine learning. The major is not the critical variable here, I feel. I think that a solid math background (probability, analysis, linear algebra) and a solid programming background and a solid computer science background are what you need. It does not matter where you get that from. Would a major in computer science be mandatory (i.e. 50% of my degree)? Or could I minor in CS (25% of my degree) and fill up the other subjects with Math/Stats? I'm not sure about physics - there's an opportunity cost to picking physics subjects and I wouldn't want to sacrifice things like advanced linear algebra, real analysis and mathematical statistics to learn about fluid flow PDEs and classical mechanics (for example) -- am I mistaken here?
(Sep 04 '13 at 09:17)
James J
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Why do you say that excluding mathematics would result in a shaky foundation in real analysis? Is there a specific topic you're especially worried about missing out on? Besides point-set (general) topology again is there something specific you're worried about not being able to understand?
@ChrisSimokat I have no idea specifically. I have just read on forums that people recommend real analysis as a subject for machine learning, which is taken through the mathematics faculty.
There are advanced courses in mathematical statistics in some programs that use many of the same measure concepts as in real analysis. Both come from the common starting point of having done some work in advanced calculus (a first rigorous proof course usually a review of what you learned in calculus hence the name). Some real analysis topics can come up if you read on statistical limit theory (think like topics on different types of convergence). Now granted the mapping isn't injective, but someone with that sort of background can readily pick up any real analysis text and run with it. I wouldn't get too hung up on the specifics in the differences unless you find yourself more interested in the specifics in a mathematics real analysis course as opposed to statistical limit theory or measure based mathematical statistics.