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I NEED A GRADUATE DEGREE.

What mathematics do I need to study before thinking about a graduate degree in machine learning?

  • Coming from a background in economics/game theory, I'm concerned I don't have the mathematical chops to pull a higher degree in machine learning. What are the basic math courses I'd need to be able to study in this field?

  • Answer:

    The key ingredients are: Matrix algebra: most machine learning models are represented as matrices and vectors. Concepts like eigenvectors and singular value decomposition appear all over the place. Bayesian statistics: probability, Bayes' rule, common distributions (e.g., beta, Dirichlet, Gaussian), etc. Multivariable calculus: most learning techniques use gradients and Hessians at their core to fit parameters. (If you want to get fancier, study numerical optimization.) Information theory: entropy, KL divergence, etc. Just the basics here. In limited cases, higher-level math can be useful. E.g., to understand manifold learning, you'll want to know some basic notions from geometry and topology. Occasionally abstract algebra is used (e.g., see "expectation semirings" for learning on hyper-graphs). I would learn these as-needed, but if you have a chance to learn them early it can't hurt. The first three are usually taught as separate courses at a university. Information theory you can pick up yourself without much trouble.

Brandon Ballinger at Quora Visit the source

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Machine learning is a field of it's own, with it's own algorithms and techniques.  Stats, linear algebra, and Fourier transforms are a start, but PhDs are being written by people creating new mathematics to better solve machine learning problems.

Jeff Nelson

Each ML algorithm has its own requirements, but in general you'll need Linear Algebra, Multivariate Calculus and Statistics.

Rafael Pinto

If you've studied Economics, then you should be well-versed in Real Analysis and Convex Optimization. Machine Learning folks, typically, use Discrete Mathematics, so there's a lot of Linear Algebra and Graph Theory. Since ML is trying to solve NP-Hard problems, the focus is more on Approximation Algorithms, instead of Convex Opt that Economists care more about. Perhaps the greatest overlap is between Machine Learning and Econometrics. Both are built upon Statistics. ML is focussed more on prediction, whereas Econometrics is about inferring Causality. A solid foundation in Probability and Statistics is necessary for Machine Learning. If you're interested in Algorithmic Game theory, an emerging branch of Machine Learning, you'd want to look closely at computing Nash equilibria. In that field, there's emphasis on interior point methods and calculus. So, if you're from an Econ background, you know more Math for Machine Learning than you think. The topics that you might want to brush up on are: - Discrete Mathematics and Approximation Algorithms. Proof techniques esp. proof by Induction. - Bayesian Statistics: which should be covered in any Advanced Econometrics course.

Debajyoti Ray

On top of many mentioned basics I found Functional Analysis to be very useful in many cases. Many extensions of standard methods often appear straightforward to me because of more general theorems. Especially a deep understanding of L^p spaces helps a lot (of course you need not take a course in Functional Analysis but I am sure that no one will regret it).

Arthur Gerigk

I think we all concur with the formula machine learning =stat+optimization and graphical model represented by graphical model : probability --> graphical model <---graph theory. So you should learn stat, optimization (linear algebra+ calculus), and some graph theory is optional !

Tran Dinh Cuong

http://measuringmeasures.com/blog/2010/3/12/learning-about-machine-learning-2nd-ed.html This blog post does a pretty thorough job of explaining the mathematical background required for machine learning. It also lists reference books for each area. I found it pretty useful.

Vijayaraghavan Apparsundaram

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