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Learning Math for Machine Learning

blog.ycombinator.com

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Re: Learning Math for Machine Learning

#91

Post by EnderMB »

andai wrote: post #87
_spoonman wrote: post #62

Earlier quoted context omitted.

We should find or start a Slack / Discord where we go through a math textbook and conquer our fear of mathematics together.

Oh man, this needs to exist.

Seconded/Thirded.

Hell, I have a CS degree, and my Maths knowledge is horrific. I didn't take Maths at A Level, so I stopped learning any Maths at 16. The course had Maths, but it's surprisingly easy to brute force a solution, and that was a good ten years ago now.

My goal for years has been to learn enough Maths to be able to read Introduction to Algorithms and TAOCP without aid, and recently to be able to better understand ML, but the more I try the more I realise that it's a multi-year investment.

Re: Learning Math for Machine Learning

#92

Post by physicsguy »

throwawaymath wrote: post #36
cs702 wrote: post #5

This is excellent. Thank you for taking the time to write it. I don't know what is it about math -- especially when it involves manipulation of symbols as opposed to pictures or lay language -- that turns off so many people. The fact that so many software developers "don't like math" is ironic, because they're perfectly happy to manipulate symbols such as "x", "file", or "user_id" that stand in for other things every…

> The fact that so many software developers "don't like math" is ironic, because they're perfectly happy to manipulate symbols such as "x", "file", or "user_id" that stand in for other things every day. The entirety of mathematical knowledge is very much like a gigantic computer language (a formal system) in which every object is and must be precisely defined in terms of other objects, using and reusing symbols like…

> Meanwhile a professional programmer has to become good at things that mathematicians and scientists don’t have to care about, like version control or the idiosyncrasies of a specific language.

Really depends on what kind of mathematician or scientist you are to be honest though. How good is someone's data analysis of an experiment if they can't reproduce it? Or if they've got 6 different versions of an application with 100k lines of code in a single file, each labelled "code_working(1).f90", "code_not_working.f90", etc... These are real problems with what people actually do in science; software development skills are poor and people do things badly.

There're organisations like Software Carpentry globally and the Software Sustainability Institute in the UK which exist to try and promote some thought about developing software as researchers, and making the software sustainable in the long term rather than letting it die every time a PhD student leaves.

Re: Learning Math for Machine Learning

#93

Post by amorphous »

Just wondering if someone had a similar experience: I absolutely loved Math in school, zipped through the classes, always one of the best.

Then things changed at university (studying computer science) and I completely lost interest. Not sure why (bad teacher, going from being best in class to being average, the math at uni different from school).

Now, much later, I regret not having followed through and miss the beauty of Math. I'm re-discovering it and wondering how I could use more of it in my work.

Re: Learning Math for Machine Learning

#94

Post by SpaceManNabs »

imh wrote: post #74
SpaceManNabs wrote: post #22

My bullet list, which might be too ambitious and theory-focused, but this is what I used from my physics background. Learn some: Calc up to 3 (you can skip some of the divergence and curl stuff) Linear algebra (no need for Jordan change of basis) Real analysis Intermediate probability theory (MAE, MAP, conjugate priors minus the measure theory stuff) A little bit of differential geometry (at least geodesics. This is…

Can you give any recommendations for a little bit of differential geometry?

This is a little difficult for me since I learned it mostly in the sense of general relativity (which is why I said some differential geometry). For that course, I mostly used the instructor's lecture notes. However, the books for the course were:

Hartle, James B., Gravity: An Introduction to Einstein's General

Schutz, Bernard, A First Course in General Relativity

The first few chapters would be all you need, but they don't include the nice things I learned from the lecture notes like how to derive the gradient, divergence, and curl in any curvilinear coordinate system by using the Christoffel symbols.

Sorry that I can't be of much more help.

Re: Learning Math for Machine Learning

#95

Post by jessaustin »

woolvalley wrote: post #76
jessaustin wrote: post #68

Earlier quoted context omitted.

I attended a not-superb high school in rural Missouri, and we studied proof by induction in 11th grade, before calculus in 12th. (Only over the naturals, but that's enough to get the flavor...) Lemmas came in 10-grade geometry, although frankly I may not understand what you mean because that's not really a full "concept", just kind of an arbitrary detail. That was the early 90s, though, so perhaps standards have slip…

My recollection is vague, since it was quite a while ago, but there were other things that weren't introduced in my high school curriculum that I remember my calculus textbook containing. I'm glad your school taught you proof of induction and other such things although. I also remember talking to my classmates about how near indecipherable our calculus textbook was.

First semester of college, I took multivariate. That was kind of a mess, because instead of a textbook we got a "bound" compilation of our professor's notes that he was trying to turn into a textbook. It has been some time, but I kept lots of math books from college, and I specifically threw that thing out. My recollection is that it was pretty much worthless.

Re: Learning Math for Machine Learning

#96

Post by soVeryTired »

smallnamespace wrote: post #70
throwawaymath wrote: post #48

Earlier quoted context omitted.

Can you talk about the use of group theory for computer vision or crystallography a bit? I'm familiar with the math but I'm not familiar with group theory's applications in those areas. That sounds pretty interesting. Is it primarily group theory, or does it so venture into abstract algebra more generally?

For crystallography, the use of group theory in part originates in X-ray crystallography [1], where the goal is to take 2D projections of a repeating 3D structure (crystal), and use that along with other rules that you know to re-infer what the 3D structure is. Repeating structures have symmetries, so seeing the symmetries in your diffraction pattern inform you of the possible symmetries (and hence possible arrangeme…

I thought the work on the structure of DNA used Fourier analysis more than group theory.

I know harmonic analysis in general combines the two, but I'm sure Crick and Watson could have done their work without knowing the definition of a group.

Re: Learning Math for Machine Learning

#98

Post by tenaciousDaniel »

_spoonman wrote: post #62
tenaciousDaniel wrote: post #46

Earlier quoted context omitted.

Awesome. I had a really difficult time with math in HS, and never pursued it at all in college, so even though I'm a programmer my math skills are barely at a high school level. I'd love to get into ML but the math keeps me at bay.

We should find or start a Slack / Discord where we go through a math textbook and conquer our fear of mathematics together.

holy crap that's an amazing idea

Re: Learning Math for Machine Learning

#99

Post by jacobolus »

throwawaymath wrote: post #47
g9yuayon wrote: post #45

I'm kinda curious why so many people think that Linear Algebra Done Right is an introductory book for beginners who have math anxiety. Don't get me wrong, the book is great and I enjoyed working it through. It was a magical experience when I saw how simple it was to prove some seemingly hard theorems by just linking the right definitions and theorems. That said, the book does require certain level of math maturity as…

Speaking as one of the people who recommended it in this thread: I don't think math anxiety is the right focus for which textbook to choose. More precisely, I don't think you should try to solve that problem by getting a different linear algebra textbook. To put it bluntly, someone with math anxiety probably just doesn't have the mathematical maturity for linear algebra yet. In that case they'd be doing themselves a…

Tools from linear algebra can be accessible and useful to many people who don’t want to (or are not yet prepared to) prove nontrivial theorems. Indeed, a book like Axler’s should probably be used in a second semester-long linear algebra course for typical undergraduates wanting to study abstract mathematics; a gentler more concrete introduction would probably be better for students without previous exposure to linear algebra or hard mathematical thinking. For engineers or others who want to use linear algebra in practical contexts, something like Boyd & Vandenberghe’s new book might be a better for a first (or even second) course than Axler’s book, https://web.stanford.edu/~boyd/vmls/

Elkies’s post is in the context of a course for very well prepared and motivated first-year undergraduate pure math students who are racing through the undergraduate curriculum because most of them intend to take graduate-level courses starting in their second year.

Those two audiences are very far apart.

Re: Learning Math for Machine Learning

#100

Post by jlelonm »

EnderMB wrote: post #91
andai wrote: post #87

Earlier quoted context omitted.

Oh man, this needs to exist.

Seconded/Thirded. Hell, I have a CS degree, and my Maths knowledge is horrific. I didn't take Maths at A Level, so I stopped learning any Maths at 16. The course had Maths, but it's surprisingly easy to brute force a solution, and that was a good ten years ago now. My goal for years has been to learn enough Maths to be able to read Introduction to Algorithms and TAOCP without aid, and recently to be able to better un…

Fourthed(?)

What's a linear transformation? I get that it's f(x + y) = f(x) + f(y) and f(cx) = c * f(x)... but what does that really mean?

Why is the dot product equivalent to ||a||*||b|| cos C? I really have no idea, I just know the formulas.

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