Books on Machine Learning without a strong math background required

  • #1

gillouche

Gold Member
25
7
Hi everyone,

I am a software developer (bachelor's degree in Europe, different than a bachelor's degree in the US I believe) and I don't have a strong math/physics background but I am willing to learn.

For a few years now, I have been really interested in machine learning but until now, I only read blog posts and examples in python. Now, I would really like to learn the maths and get the intuition behind ML so I need resources adapted to my maths background.

I haven't started working on Multivariable calculus, linear algebra and differential equations on Khan Academy yet so I have a lot of work to do. I also worked on paul's online notes (http://tutorial.math.lamar.edu/) except Calculus III and diffeq.

I read online that the following maths are required to properly learn machine learning concepts

1) probability and statistics
I have Mathematical Methods in the Physical Sciences from Mary Boas, I don't know if that's enough.
any online resources, books (free or not) that you would recommend ?

2) Linear algebra
I have two books from Serge Lang :
Introduction to Linear Algebra Undergraduate Texts in Mathematics
Linear Algebra Undergraduate Texts in Mathematics

I plan to complete that with Khan Academy and his MIT lectures. I guess that for linear algebra, I will be fine once I finished working on these resources.

3) Calculus / multivariable calculus ?
I learned with Khan Academy / Patrick JMT but I never worked with other resources. I guess I should review that topic with a more formal book. Any advice ?

4) Optimization
I don't have any resources treating this subject.

Thank you very much.
 
Last edited:

Answers and Replies

  • #3
Hi,

I know there are plenty of books on the subject. That's why I am looking for advice for books which do not require a strong mathematical background and would still be good to get knowledge and intuitions on the required maths for ML.

If I search "calculus" on google books, I get Spivak's. That's not really the kind of books that I am looking for.

I am already a gold member and yes, I would have used amazon link if available where I can order.
 
  • #5
Buffu said:
How about https://www.amazon.com/dp/1441923225/?tag=pfamazon01-20 and https://www.amazon.com/dp/0521592712/?tag=pfamazon01-20 ?
I don't think that either of these satisfies
gillouche said:
...I am looking for advice for books which do not require a strong mathematical background and would still be good to get knowledge and intuitions on the required maths for ML.
In the preface to All of statistics the author writes that the book is suitable for graduate students in computer science or honors undergraduates in math, statistics or computer science. I checked it out from the library once and do not believe that the OP is prepared.

Likewise, i own a copy of the book by Jaynes. It is not easy reading, and has as much philosophy as probability. According to the preface, it is "addressed to readers who are already familiar with applied mathematics, at the advanced undergraduate level or preferably higher,"

I do not know what book, if any, would be appropriate for the OP, but I do not think either one of those would be helpful.

Jason
 
  • #6
gillouche said:
Hi everyone,

I am a software developer (bachelor's degree in Europe, different than a bachelor's degree in the US I believe) and I don't have a strong math/physics background but I am willing to learn.

For a few years now, I have been really interested in machine learning but until now, I only read blog posts and examples in python. Now, I would really like to learn the maths and get the intuition behind ML so I need resources adapted to my maths background.

I haven't started working on Multivariable calculus, linear algebra and differential equations on Khan Academy yet so I have a lot of work to do. I also worked on paul's online notes (http://tutorial.math.lamar.edu/) except Calculus III and diffeq.

I read online that the following maths are required to properly learn machine learning concepts

1) probability and statistics
...

2) Linear algebra
...

3) Calculus / multivariable calculus ?
...

4) Optimization
...

If you want something structured for multi-variable calc, you may want to work through the assignments here:
https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/

key things to learn are how to think about derivatives in higher dimensions, do nested integrals (basically nested for loops), lagrange multipliers, chain rule, taylor polynomials. Taylor polynomials (not series but polynomials) believe it or not are basically the all access pass for most optimization techniques in ML. A lot of the stuff in multi-variable calc will not be needed -- e.g. spherical coordinate systems, line integrals, surface integrals, etc. I don't think really ever come up in machine learning -- you're basically working in rectangular coordinates and need to be able to interpret nested integrals. (Nested integrals also will come up in the below probability courses.)

probability, one of the courses recommended here:
https://www.physicsforums.com/threa...swer-sheet-in-statistics.921188/#post-5810893
You need to do multi-variable calc first though. I am biased towards the stuff from MIT like 6.041 (and 6.041x on edx). This can be mind-bending stuff so doing lots of exercises (with solutions available) is key.

If there's one topic you were going to beat with a hammer on your list, it probably should be linear algebra, which comes up again and again in various forms for ML. My advice would be to pick one of the sources you mentioned and work through it and then ignore the other linear algebra sources on your list. Step two would be to work through the first 7 chapters of Linear Algebra Done Wrong, freely available by the author here: https://www.math.brown.edu/~treil/papers/LADW/LADW_2017-09-04.pdf . It still has my favorite walkthrough of spectral theory that I've seen. I wouldn't recommend it as a first book in linear algebra, but that's probably the only negative I'd say about it.

I woudn't worry too much about optimization for the time being -- you should pick it up as you go along in ML. I do trust that you are familiar with Dynamic Programming, though, as part of your CS background.
 
  • #7
Although ML includes many topics, this video gives an extremely intuitive explanation of how a neural network works - the heart of deep learning. This will convince you of the need for linear algebra.


For linear algebra, I highly recommend the work of "3blue1brown". Arguably the best guy available for explaining the intuition behind the math.
https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

Since your goal is to get to the basics of ML, and the math is just a stepping stone, I have two suggestions for LA texts that don't emphasize proofs or rigour:
(1) https://www.amazon.com/dp/0980232775/?tag=pfamazon01-20
I find Strang tries to convey the intuition more than other texts. Solutions to problems are available online as well.
http://math.mit.edu/~gs/linearalgebra/
If you prefer to learn by watching lectures, it goes hand in hand with his MIT courseware lectures.
(2) https://www.amazon.com/dp/0199654441/?tag=pfamazon01-20
His approach reminds me of people tend to learn these days from the web. Lots of worked out examples, and many FAQ-like question/answer sections.
Solutions are available here:
http://global.oup.com/booksites/content/9780199654444/

For probability, consider this book. It also focuses on intuition.
https://www.amazon.com/dp/1523318678/?tag=pfamazon01-20
Like Morin's other texts on classical mechanics and electromagnetics, he has many worked through examples.

For calculus, Paul's online pages are as good as any and some will argue among the best. A hardcopy alternative might be Stewart's Calculus - a good choice if rigor and proofs are less important than picking up the ideas quickly. Calculus in the context of ML will help with things like probability distributions or calculating the area under a Bell curve, etc., etc.

Finally, here is a good book on deep learning (fun fact: one of Elon Musk's favourites):
https://www.amazon.com/dp/0262035618/?tag=pfamazon01-20

There are reading group videos for most chapters on youtube and is led by the author:


Also, ML often involves Bayesian analysis. Here is a respected source that is heavy on exposition and also makes use of a freely available language called R which is in wide use among data scientists:
https://www.amazon.com/dp/0124058884/?tag=pfamazon01-20
 
  • #10
Thank you very much to you all for the valuable information, that's exactly what I was looking for.

I am highly motivated to learn the maths needed as long as it is not too abstract.

Thanks again.
 
  • #11
I know this post is several months ago. I just came across this course, which somebody told me he was working on. https://www.edx.org/course/essential-math-machine-learning-python
It's titled Essential Math, and from the description - it looks like it let's you get some idea about the math you would need, rather than a full course. But it may be worth a look for somebody who has not taken any Calculiua,. etc
 

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