How to Machine Learn

https://docs.google.com/document/d/1YN6BVdReNAYc8B0fjQ84yzDflqmeEPj7S0Xc-9_26R0/edit?usp=sharing

by gwulf • 11 years ago

136 26 11 years ago

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I'm a freshman in university right now, how is linear algebra helpful in computer science? I'm finding it hard to stay motivated as I can't think of any uses outside of graphics. Maybe I'm just not far along in the course though.

hiddencost3• 11 years ago

http://math.stackexchange.com/questions/344879/how-does-line...

Pretty much all of machine learning relies on linear algebra.

Most scientific computing relies on lI near algebra.

Graph algorithms often use linear algebra.

If you just want to be a Web Dev or an app developer, it probably doesn't matter, tho.

But if you just want to do Web Dev or mobile apps then you don't really need most of computer science.

fa4• 11 years ago

Well, if I remember my university's beginner linear algebra course, there were many topics on the syllabus only due to historic accident, ancestor worship, and theoretical necessities: I remember parallelepipeds, Cramer's rule, solving eigensystems by solving for a polynomial's zeros... Let me tell you how many times I've used parallelepipeds, Cramer's rule, or found eigenvalues via the quadratic formula in the 12 years since linear algebra (and a career in statistical signal processing and machine learning): zero, zero, and zero. Most things in college are important only to the extent that they're gatekeepers for what's really important. What hiddencost says is true, but very little of what you're learning in class is relevant to those important and interesting things. Sorry: college sucks.

rhgraysonii• 11 years ago

A good starting point is singular value decomposition [0]

0. http://en.wikipedia.org/wiki/Singular_value_decomposition

jostmey• 11 years ago

A lot of people don't appreciate the utility of Linear Algebra because they fail to see how the core theorems generalize beyond Cartesian coordinates. Sure, the basic operators of a vector space such as "+" and "*" look boringly familiar, but these operations can be overloaded to carry out other calculations just like in computer programming. The fact that you can represent any "vector space" with a basis set and that every possible basis set for that vector space will have the same dimensionality is pretty cool and useful.

gms7777• 11 years ago

Linear algebra comes up all the time in advanced courses. Certainly in graphics, but also if you do any machine learning, optimization, probabilistic algorithms, any sort of scientific computation. I never took a linear algebra course, convincing myself that I could just pick it up as I went along and getting into grad level computer science courses was ultimately a rather painful experience because of this. If I were you, I'd try to take it seriously and really try to develop an intuitive feel for linear algebra because (depending on what courses you want to take), it can really save you time and headaches in the future.

powerset• 11 years ago

A nice little pep talk motivating study of linear algebra and why it's useful (e.g. pagerank):

http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebr...

j2kun4• 11 years ago

I write a blog on math and programming and I see linear algebra applied every day.

1. Ranking in search engines (more generally, any kind of random walk analysis) [1]

2. Fourier analysis, and as a consequence most signal processing involves some understanding of linear algebra because integrals are linear. [2]

3. Regression [3] and more generally linear modeling of anything.

4. Facial recognition [4]

5. Community detection [5], where most leading methods analyze the spectrum of a graph to find communities. In fact, applied network science in general has a ton of linear algebra.

6. Greedy algorithms are characterized by a kind of generalization of linear systems [6]

7. Linear programming, perhaps the most applied piece of mathematics ever, needs a strong foundation of linear algebra [7]

8. All of quantum computing is literally just linear algebra [8].

9. Cryptography has a ton of linear algebra in it, and a large portion of the techniques are reasoned about with linear algebra.

10. Most of calculus relies on linear algebra, most importantly optimization [9]

11. Recent data analysis techniques based on topology do so through linear algebra [10]

12. Coding theory, including the algorithms used to correct errors on DVDs. Basically, any time you want to encode data so that you can recover from white noise, you're going to use a linear code. [11] This includes compression techniques.

13. Of course graphics.

I could go on...

[1] http://jeremykun.com/2011/06/12/googles-pagerank-introductio...

[2] http://jeremykun.com/2012/07/18/the-fast-fourier-transform/

[3] http://jeremykun.com/2013/08/18/linear-regression/

[4] http://jeremykun.com/2011/07/27/eigenfaces/

[5] http://jeremykun.com/2014/05/19/community-detection-in-graph...

[6] http://jeremykun.com/2014/08/26/when-greedy-algorithms-are-p...

[7] http://jeremykun.com/2014/06/02/linear-programming-and-the-m...

[8] http://jeremykun.com/2014/12/08/a-motivation-for-quantum-com...

[9] http://jeremykun.com/2013/11/30/lagrangians-for-the-amnesiac...

[10] http://jeremykun.com/2013/04/10/computing-homology/

[11] http://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_corr...

fa4• 11 years ago

Have you done one on compressive sensing and the functional analysis roots of that field?

anindyabd• 11 years ago

The website for the project linked to on the first line is based on this Bootstrap template: http://startbootstrap.com/template-overviews/grayscale/. At least they could have changed the background photo!

gwulf• 11 years ago

Good find! The goal was to wrap the feature engineer scripts up with a front end, so design was an after thought.

raz32dust• 11 years ago

Useful list. I would recommend adding one more resource for linear algebra/machine learning:

I absolutely enjoyed learning Linear Algebra from these beautiful lectures by Prof. Gilbert Strang (MIT): https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD9101...

Seriously, I gained a new found appreciation for Linear algebra after going through these lectures. You should go over some of these lectures even if you already know linear algebra - it might give you insights you never had before (it did, for me). Absolute must-watch if you are into machine learning or related areas.

How to Machine Learn

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