Considering that some CS graduates haven't got much in depth knowledge about the mathematical concepts in Machine Learning, which option should be better ?
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5$\begingroup$ I doubt this has a clean, unconditional answer? $\endgroup$– Matthew GunnCommented Sep 27, 2016 at 23:18
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$\begingroup$ I would like to put the AIC and BIC advocates in a sealed room to see who survives their self-proclaimed objectivity. Yes, of course there is opinion. This is research, just that everyone should do this research for his own particular case, as in reality the options are all personal. All I was trying to do in answering was help Nick out to give him a boost at looking for himself at curricula. I think that the more valid objection to this type of question is not that opinion is involved, but that it is off topic. $\endgroup$– CarlCommented Sep 28, 2016 at 19:50
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$\begingroup$ @MatthewGunn And you would likely be incorrect. Machine learning is clearly a subset of applied mathematics, and applied mathematicians are clearly mathematicians whose role is to supply and advocate mathematics usage to many fields, including and definitely not limited to machine learning. $\endgroup$– CarlCommented Sep 29, 2016 at 15:46
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$\begingroup$ @Carl I think we're actually more in agreement? You write, "...everyone should do this research for his own particular case, as in reality the options are all personal." I agree. I think we're both saying that the OP's personal, unique circumstances should factor into the decision. I doubt that an M.Sc. in Applied Math or a M.Sc. in Machine Learning is almost always better than the other? I doubt that this question can be sensibly answered in an unconditional way? The decision probably shouldn't be a function merely of the programs but of the programs and the person. $\endgroup$– Matthew GunnCommented Sep 29, 2016 at 16:09
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$\begingroup$ @MatthewGunn True enough, but this question will be removed if someone does not edit it. I did edit it to be more information based, but my edit was rejected. What to do? Should I change the question to be more curriculum based and re-post it? $\endgroup$– CarlCommented Sep 29, 2016 at 19:43
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Well, that would depend where. More information about machine learning is given here What math subjects would you suggest to prepare for data mining and machine learning? But consider the following:
At the University of Waterloo Applicants for the applied mathematics masters program MMath (thesis) normally have an honours bachelors degree in Mathematics. We also welcome applications from students who have completed a degree in Science or Engineering, with a strong concentration in mathematics. Students who have a strong academic record but who have some gaps in their Applied Mathematics background may be admitted subject to the requirement that they complete a selection of fourth year undergraduate courses as part of their graduate program. Minimum grade point average: 78% (in Canada) or equivalent.
At Carnegie Mellon University The curriculum for the Masters in Machine Learning requires five core machine learning courses, and two electives.
These core courses together provide a foundation in machine learning, statistics, probability, and algorithms.
10-701 Introduction to Machine Learning or 10-715 Advanced Introduction to Machine Learning
10-702 Statistical Machine Learning
36-705 Intermediate Statistics
Plus any two of the following courses:
10-708 Probabilistic Graphical Models
10-725 Convex Optimization
15-826 Multimedia Databases and Data Mining
15-750 Algorithms or 15-853 Algorithms in the Real World
MS students are required to complete a Data Analysis Project (DAP). The Data Analysis Project will be concluded by a written report and an oral presentation in the ML Journal Club.
What that means, in effect, is that machine learning is an application of mathematics that is well developed, and that applied mathematics is a general powerful discipline that prepares one for all eventualities, including machine learning :) So, it you will, if your mathematics is not that strong, machine learning will include only a subset of the math you will need for applied mathematics. To put it another way, applied mathematics is taught by people who may throw highly theoretical material at you, i.e., pure mathematics.
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$\begingroup$ So you're suggesting that the best option is applying to the ML Master's course due to it covering a small subset of Applied Mathematics. If, though, I'm considering to apply to a Machine Learning PhD (which needs a good understanding of Calculus, Numerical Analysis, Linear Algebra, Optimization and Probability Theory), would I be covered with the ML Masters ? $\endgroup$ Commented Sep 28, 2016 at 2:30
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3$\begingroup$ I think applied math may include Hilbert spaces, tensor calculus, advanced linear algebra, analysis, transforms (e.g. Radon transform), and topology but I wouldn't know exactly, look up some curricula and find out. In any case, your best defense against a lack of knowledge of mathematics is to learn more. Avoiding math will not help you solve problems. Besides, Nick, you have a head start on the Greek letters used:) $\endgroup$– CarlCommented Sep 28, 2016 at 2:43