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Mathematics for Machine Learning

Coursera · Imperial College London · 106 HN points · 4 HN comments

HN Academy has aggregated all Hacker News stories and comments that mention Coursera's "Mathematics for Machine Learning" from Imperial College London.
Course Description

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science.

In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them.

The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting.

The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require Python and numpy knowledge.

At the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning.

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This course is offered by Imperial College London on the Coursera platform.
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On a related note, I'm curious if anyone has taken the Mathematics for Machine Learning ( courses on Coursera, and whether it really covers enough to be comfortable with ML. The course bills itself as enough math knowledge for folks who barely remember high school math.
I have completed all three courses in the series. It was a good supplement to other resources, especially 3blue1brown's Linear Algebra course on youtube[0] (mind-blowing, do check it out) but I wouldn't recommend it as a first course. The first two courses weren't rigorous enough for my taste (I am yet to find a rigorous course on Coursera), but the third was pretty good. You should take up books if you are serious.

MIT OCW Scholar(independent study) course on Linear Algebra by Prof. Strang[1] is really good and is designed for self-study. If you have the time, you could look up Coding the matrix[2] too. I read probability from Mathematics for Computer Science-MIT[3] and also referred Khan Academy[4] and PennState STAT 414/415 [5] for statistics and probability. StatQuest channel[6] on Youtube has handwavy but easy to understand videos on statistics for ML too. The Deep learning book[7] by Ian Goodfellow et al. has a couple of chapters at the beginning that gives you a fairly good idea of the mathematics required to get into Deep learning. Communities like r/AskStatistics and r/statistics on Reddit were really helpful when I got stuck.

I also chanced upon Mathematics for Machine Learning[8] book recently and it seems to be good. It has a chapter on optimization that is left out in most books but skips statistics.

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These are great insights! Thanks so much. Do you think it's worth going through pre-calc/calc deeply? I assumed I should do that first, but it would take quite a while (I haven't taken calc in ~8 years and barely remember more than the basics).
Essence of calculus[0] by 3blue1brown for the basics and the second course in the Coursera Mathematics for Machine Learning would let you get started. You would rarely need calculus more advanced than that covered in the above, and if need be you will be in a position to look it up quickly. If you can sustain your interest in ML over a long period of time and are in no hurry, I would recommend going through all the math mentioned. If you are a top-down learner, the course on ML and deep learning for coders will get you started head-first. All the best!

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I have. It’s great because it’s developed using geometric intuition (a la 3b1b). Just missing probability/stats.
Looking at the courses, it doesn't cover calculus and probability. That's two topics that you should already know and that you might not have mastered in High School. Otherwise, you are good to go.
Nice article. Would you recommend this MOOC? It doesn't focus on probability or statistics though. If not, is there any other MOOC you would suggest?
You should consider taking this course series "Mathematics for Machine Learning" from coursera.

However, if you know the very basics of matrices (multiplication, transpose) and calculus (derivatives of basic functions, and partial derivates, and chain rule) I'd highly recommend first trying basic applied ML before diving deep into the math. It'll help you see where the math you're learning is actually used, as you learn them.

Try first, then try this "math for ML" course.

Apr 09, 2018 · 106 points, 10 comments · submitted by nafizh
I've been looking for something like this to brush up/add to my math knowledge; can anyone recommend this course or would you recommend some other way?
Many ML methods require solid knowledge of probability and statistics. Strangely this course does not cover that.
I agree - it looks equivalent to perhaps 1st year mathematics in Australian university or 2nd year 1st semester if I'm being really generous.

This definitely isn't sufficient for machine learning, but it is a start.

It is good for understanding many ML algorithms and how they work internally. So in my opinion it's enough.
Ah, I should've figured that out myself from looking at the contents. I might try it out and combine it with some reading of my old statistics book or some other means. Thanks!
My impression from reading about a few ML techniques (such as Neural Nets or Support Vector Machines) is that this class of ML algorithms relies heavily on regression techniques that are, at their core, nonlinear optimization problems. This means finding local maxima and minima for systems of nonlinear equations, either analytically or through gradient descent. Either way, you're going to need to deal with a system of partial derivatives, which means you need to understand vector calculus and linear algebra. If that's the focus of this course, then I'd say it does make sense.

I understand what I described above is a subset of ML, and I generally do agree with you that a solid background in probability and stats is important for people who plan to do a lot of ML.

Note - another possible objection here is that all "STEM" fields require calculus through differential equations and linear algebra. That's pretty much the common thread for most majors generally grouped together as STEM fields. So calling this "mathematics for machine learning" could be a little strange. If we're going to call vector calc and linear algebra "mathematics for ML", why aren't we calling it "math for physics", or "math for engineering"... I think that part of what is going on is that ML has gotten very popular, and people are starting to ask what the essential math background is, and are discovering that it's, well, pretty much the two year science and engineering track calculus you'd take at most universities.

Funny, you used the term “regression”. People without stats 101 background will not know what you’re talking about.
Link is dead


This course is from Imperial College in London. It's typically ranked as one of the top 3 universities from the UK. Finally it has joined the ranks of doing a coursera course. Other noticeable absentees from coursera are Oxford and Cambridge. I know they do provide a few of their own though open courses.

I guess universities shouldn't be forced to give open courses, but it is a fantastic thing that US showed was possible and I hope that more UK universities follow suit.

Oxford actually has one course on EdX:

My understanding is that, like many MOOCs, it is largely department/faculty driven rather than a strategic or philanthropic move by the university overall.

Take a look at the Coursera specialization: Mathematics for Machine Learning [1]. The specialization isn't free but you can certainly apply for financial aid.


Yes! It's a new course that will be open for enrolment soon. I think it's exactly what most people here are looking for.

There is the financial aid and normally there is the option to watch the lectures and see the assignment for free. On the other hand, the cost of the courses rarely exceeds $50.

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