Learning Math for Machine Learning

To play devil's advocate, (EDIT: an intuitive understanding of) probabilistic reasoning (probability theory, stochastic processes, Bayesian reasoning, graphical models, variational inference) might be equally if not more important.

The emphasis on linear algebra is an artifact of a certain computational mindset (and currently available hardware), and the recent breakthroughs with deep neural networks (tremendously exciting, but modest success, in the larger scheme of what we wish to accomplish with machine learning). Ideas from probabilistic reasoning might well be the blind spot that's holding back progress.

Further, for a lot of people doing "data science" (and not using neural networks out the wazoo) I think that they can abstract away several linear algebra based implementation details if they understand the probabilistic motivations -- which hints at the tremendous potential for the nascent area of "probabilistic programming".

In our Data Scientist Track (https://www.dataquest.io/path/data-scientist?), I specifically focused on teaching K-nearest neighbors first b/c it has minimal math but you can still teach ML concepts like cross-validation, and then I wrote Linear Algebra and Calculus courses before diving into Linear Regression.

https://www.dropbox.com/s/lh23y44dsg96xpv/Screenshot%202018-...

For intuition, particularly if you care about vision applications, I think one field of math which is severely underrated by the community is group theory. Trying to understand methods which largely proceed by divining structure without first trying to understand symmetry has to be a challenge.

I'm biased; my training was as a mineralogist and crystallographer! But the serious point here is that much of the value of math is as a source of intuition and useful metaphor. Facility with notation is pretty secondary.

And of course, you're not going to get very far with probability theory and stochastic processes unless you have a mature understanding of analysis and measure theory :)

This comment exchange neatly demonstrates the intrinsic problem. Most of these articles start off much like this one does: by assuming "basic comfortability with linear algebra." That sounds straightforward, but most software engineers don't have it. They haven't needed it, so they haven't retained it even if they learned it in college. It takes a good student a semester in a classroom to achieve that "comfortability", and for most it doesn't come until a second course or after revisiting the material.

If you don't already have it, you can't just use StackExchange to fill in the blanks. The random walk method to learning math doesn't really pan out for advanced material because it all builds on prior definitions. Then people like you make a comment to point out (correctly) that probability theory is just as important for all the machine learning that isn't just numerical optimization. But unless you want to restrict yourself to basic statistics and discrete probability, you're going to have a bad time working on probability without analysis. And analysis is going to a pain without calculus, and so on and so forth.

There are certain things you need to spend a lot of time learning. Engineering and mathematics are both like that. But I think many of these articles do a disservice by implying that you can cut down on the learning time for the math if you have engineering experience. That's really not the case. If you're working in machine learning and you need to know linear algebra (i.e. you can't just let the underlying library handle that for you), you can't just pick and choose what you need. You need to have a robust understanding of the material. There isn't a royal road.

I think it's really great people like the author (who is presumably also the submitter) want to write these kinds of introductions. But at the same time, the author is a research assistant in the Stanford AI Lab. I think it's fair to say he may not have a firm awareness of how far most software engineers are from the prerequisites he outlined. And by extension, I don't think most people know what "comfortability with linear algebra" means if they don't already have it. It's very hard to enumerate your unknown unknowns in this territory.