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Introduction to Linear Algebra for Applied Machine Learning with Python

pabloinsente.github.io

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Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#41

Post by codebug88 »

aanet wrote: post #39

This looks like an excellent resource. Thank you. The rendering of some of the Latex code does seem to be bit of a challenge; I see some intermingled code/text (on latest Mozilla on Ubuntu 18). The CPU usage also shoots up. What scripts are rendering the Latex code?

It usually takes a while to render the LaTeX code in my browser. If you scroll down immediately after entering the site you may find it looking weird. I just used mathjax syntax which supposedly renders on most browsers (my blog is hosted on GitHub, using Jekyll as site-generator). My knowledge of web-development is very basic, so I might be doing some things wrong ( ˘︹˘ )

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#42

Post by vector_spaces »

BossingAround wrote: post #25

I just recently finally bought Strang's introduction to Linear Algebra. The book itself is very dense and, dare I say, scary to a newcomer, but his videos are amazingly clear in combination with the book. I am in the beginning, but so far, I'd recommend the book. Though, the steep price (almost 100USD over here) makes it a bit difficult to recommend. I might buy Boyd’s and Vandenberghe’s Introduction to Applied Linea…

My sense is that Vandenberghe is great for getting your feet wet and building intuition, but it's not as deep as Strang in its coverage and has fewer problems. Definitely still worth reading through especially since the problems lend themselves well to working through with Julia or Python or similar.

For further reading, try Matrix Analysis and Applied Linear Algebra by Meyer.

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#43

Post by dan-robertson »

I like that this touches on some of the algebra aspects. I always find it strange when I see something about “linear algebra” that never mentions linear maps, vector spaces or bases. Perhaps the mechanics of computing with matrices is better for an introduction for people who are only interested in machine learning but the mathematician in me feels like it is important to get across that in some specific sense the numbers in a matrix are arbitrary and that the essence of the thing is simpler.

I’m a bit surprised that this doesn’t mention suffix notation, especially as multilinear maps are so common in machine learning and suffix notation is such a good way to work with them.

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#45

Post by sedeki »

redvenom wrote: post #26
gspr wrote: post #20

I was scrolling through to see if you explain how you typeset the math (notoriously hard on webpages), but I happened to instead find a small mistake. You write: "Elements of $\mathbb{R}^n$ are sets of real numbers." That is an incorrect definition. - It is inaccurate because n doesn't enter into the definition (and thus all Euclidean spaces would be the same). - You want ordered n-tuples, not sets. If you actually d…

Totally agree with this post...however, to be extremely pedantic (and thus not suitable for the article in question), a tuple in the foundations of mathematics is typically defined as a set. That is, (x,y) := {x,{x,y}}, where the latter is the set containing the element x and the set {x,y}. That is how one goes from axiomatic set theory to define tuples of numbers.

There is a big difference between your type of pedantry versus the OP... I don't think the OP was pedantic. It is simply not a set of real numbers. He did say that it was a "small mistake".

The first is more an error of understanding (for the lack of a better term), whereas talking about tuples as being de facto sets is truly about being pedantic.

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#46

Post by joppy »

redvenom wrote: post #26
gspr wrote: post #20

I was scrolling through to see if you explain how you typeset the math (notoriously hard on webpages), but I happened to instead find a small mistake. You write: "Elements of $\mathbb{R}^n$ are sets of real numbers." That is an incorrect definition. - It is inaccurate because n doesn't enter into the definition (and thus all Euclidean spaces would be the same). - You want ordered n-tuples, not sets. If you actually d…

Totally agree with this post...however, to be extremely pedantic (and thus not suitable for the article in question), a tuple in the foundations of mathematics is typically defined as a set. That is, (x,y) := {x,{x,y}}, where the latter is the set containing the element x and the set {x,y}. That is how one goes from axiomatic set theory to define tuples of numbers.

Who goes from axiomatic set theory at all, if their goal is not to be a logician/type theorist? One does not need to know axiomatic set theory to study linear algebra any more than one needs to know about semiconductors in order to program in Python.

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#48

Post by tchaffee »

gspr wrote: post #32
joshvm wrote: post #21

Earlier quoted context omitted.

Accompanying the book in the sibling comment is Strang's MIT 18.065 course which is exactly what you're after (it specifically covers linear algebra with a focus on data science and ML): https://ocw.mit.edu/courses/mathematics/18-065-matrix-method... OCW so it's free(!), including the videos and handouts.

And Strang (more than) knows what he's talking about. Unlike OP, who treats minor corrections as personal attacks and goes all defensive. This is part of the reasons why it's dangerous to replace education from established institutions with random blogs on the internet.

> This is part of the reasons why it's dangerous to replace education from established institutions with random blogs on the internet.

Please don't gatekeep education like this. I've caught teachers from established institutions in mistakes hundreds of times in my life, and often just as defensive. And I've found "random blogs" on the internet that explain things far clearer than the school recommended book. The only thing that is important is the quality of the resource, not where it came from.

Strang's free videos are great. That's the important thing to share.

(I edited to clarify which part of the parent comment I took issue with).

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#49

Post by gspr »

tchaffee wrote: post #48
gspr wrote: post #32

Earlier quoted context omitted.

And Strang (more than) knows what he's talking about. Unlike OP, who treats minor corrections as personal attacks and goes all defensive. This is part of the reasons why it's dangerous to replace education from established institutions with random blogs on the internet.

> This is part of the reasons why it's dangerous to replace education from established institutions with random blogs on the internet. Please don't gatekeep education like this. I've caught teachers from established institutions in mistakes hundreds of times in my life, and often just as defensive. And I've found "random blogs" on the internet that explain things far clearer than the school recommended book. The only…

> Please don't gatekeep education like this. I've caught teachers from established institutions in mistakes hundreds of times in my life, and often just as defensive. And I've found "random blogs" on the internet that explain things far clearer than the school recommended book.

Absolutely! And I've had medical doctors make lots of mistakes, while random blogs on the Internet have been right. Buuuut, you know.

> The only thing that is important is the quality of the resource, not where it came from.

Right. And the blog author we're discussing is flat out refusing to accept that his material has basic mistakes. That's a gigantic red flag. Again: it's not about being wrong. It's about refusing to accept that he's wrong.

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#50

Post by tchaffee »

gspr wrote: post #49
tchaffee wrote: post #48

Earlier quoted context omitted.

> This is part of the reasons why it's dangerous to replace education from established institutions with random blogs on the internet. Please don't gatekeep education like this. I've caught teachers from established institutions in mistakes hundreds of times in my life, and often just as defensive. And I've found "random blogs" on the internet that explain things far clearer than the school recommended book. The only…

> Please don't gatekeep education like this. I've caught teachers from established institutions in mistakes hundreds of times in my life, and often just as defensive. And I've found "random blogs" on the internet that explain things far clearer than the school recommended book. Absolutely! And I've had medical doctors make lots of mistakes, while random blogs on the Internet have been right. Buuuut, you know. > The o…

> Buuuut, you know.

No I don't. Could you please explain? If random blogs have helped you catch doctors making mistakes (like they have me) then it would seem to strengthen my point that gatekeeping sources of valuable information based on their origin instead of their quality is a mistaken approach.

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