4 ms·

Mathematics for Machine Learning [pdf]

327 points by yarapavan 7y ago

Anon84 7y ago
Previous discussion from April 2018: https://news.ycombinator.com/item?id=16750789 https://news.ycombinator.com/item?id=16750789
mendeza 7y ago
I am taking CS 236 (Deep Generative Models) at Stanford and this course really helped me a lot in reviewing the math I needed for the class. This is because the chapters focus on the concepts and ideas you should know, so you don't have to waste time learning everything there is to know about linear algebra and convex optimization, but the essentials for machine learning.
Nicci00 7y ago
Id be useful to have a "math for programmers book" that uses pseudo code instead of math notation. I studied math notation in 8th grade and then forgot about it.
- the_decider 7y ago
  This book (Data Science Bookcamp) uses actual Python code instead of math notation. https://www.manning.com/books/data-science-bookcamp https://www.manning.com/books/data-science-bookcamp
- TallGuyShort 7y ago
  "Coding the matrix" was the breakthrough for me in grokking linear algebra, and this is what it does. Things are explained in terms of matrices and the mathematical transformations, and then explained in terms of python data structures and a loop over the elements. And most of the examples are computer science, like rotating images.
  - uwuhn 7y ago
    I remember this course when it first came out, but didn't go through it since I didn't actually know how to program/code back then. Should I just buy the paperback off Amazon?
    - sn9 7y ago
      It's pretty cheap. I'd say go for it.
    - TallGuyShort 7y ago
      I didn't even know it was a course, I just got the book on Kindle. But I'd say go for it - as the other commenter said, it's cheap, and it doesn't require much coding knowledge, and it even explains most of what you do need to know if it's new to you. The real breakthrough is implementing the transformation in terms of fairly simple loops - which as a coder worked well for my brain. A non-coder might not find the advantage as big as I did, but I certainly don't think someone who can pick up some basic coding would struggle to understand what is being taught.
- corysama 7y ago
  Here's a start https://github.com/Jam3/math-as-code https://github.com/Jam3/math-as-code
- mkl 7y ago
  Possibly, but if you want to learn maths, then the notation is one of the smallest, easiest parts of it, and it's really helpful for the bigger, harder parts. Code is usually way more verbose than maths notation, so things get a lot bigger and it can be a lot harder to see what's going on. Learning maths notation is like learning the basic syntax of a programming language related to one you know already - there's not much to it and it doesn't take long to be able to read it comfortably. If you can already code then you know the basics and many relevant concepts already.
- Impossible 7y ago
  A Programmer's Introduction to Mathematics is probably what you're looking for. https://pimbook.org/ https://pimbook.org/
  - ah700 7y ago
    I bought the book attempted to study from it and I am not a fan. It covers topics too briefly to be called an "introduction" to mathematics. If you have a solid math background and need a refresher you may find it useful, otherwise I found MIT OCW Mathematics for Computer Science to be a much more suitable introduction, and it comes with problem sets and answers (for the 2010 course). You can also purchase the course notes in book form on Amazon. https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/readings/ https://ocw.mit.edu/courses/electrical-engineering-and-compu... solutions https://drive.google.com/drive/folders/0B4G5KBKimr07WXRlT0VKb0E0TGc https://drive.google.com/drive/folders/0B4G5KBKimr07WXRlT0VK... physical book https://www.amazon.com/Mathematics-Computer-Science-Eric-Lehman/dp/1680921223/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=&sr=#customerReviews https://www.amazon.com/Mathematics-Computer-Science-Eric-Leh...
- domnomnom 7y ago
  If you can't even learn the syntax how will you ever learn the semantics?
- ivan_ah 7y ago
  Check out this short excerpt of definitions and examples of the math "alien symbols": https://minireference.com/static/excerpts/set_notation.pdf https://minireference.com/static/excerpts/set_notation.pdf They are really not that bad once you learn their meaning + very useful shorthand (you can think of math notation as a DSL with specific expressions for math operations). Longer preview of the book: https://minireference.com/static/excerpts/noBSguide_v5_preview.pdf https://minireference.com/static/excerpts/noBSguide_v5_previ... and here is another preview of the LA book: https://minireference.com/static/excerpts/noBSguide2LA_preview.pdf https://minireference.com/static/excerpts/noBSguide2LA_previ... Both books have been pretty popular with the programming crowd. They use standard math notation, but there are lots of code examples and computing analogies, so you'll feel right at home.
sergeyfilippov 7y ago
How would you compare this book to the first part of "Deep Learning" book (by Ian Goodfellow, Yoshua Bengio, and Aaron Courville)? https://www.amazon.com/gp/product/0262035618 https://www.amazon.com/gp/product/0262035618
- zer0sugar 7y ago
  I feel obligated to interject here as I have not read the book OP linked to but I have attempted to read the paper weight calling itself a book that you linked to. I have it right here actually. It's basically total trash. They claim to show you how to do the math but at the very best all they do is restate random formulas without any explanation. It's not even good enough to serve as a refresher if you know the math. It relies very heavily on you mentally decompiling mathematical notation. I can't believe I got fooled into buying that book. If you just want to learn the math there's no easier way than to pick up some math books from half price books. They're $10 a pop. It's an affordable way to learn at your own pace.
  - random314 7y ago
    As a counterpoint, I have the book and found it to be really helpful.
    - disgruntledphd2 7y ago
      I enjoyed the book, but have a background in this area. I was amused by the suggestion that computer science undergrads could handle the book, as clearly the authors and I have met very different computer science undergrads.
      - mlthoughts2018 7y ago
        The Courville, Goodfellow and Bengio book is definitely suitable for undergraduates. In my current job, we often have new junior level (bachelor’s grads) ML hires work through that book and present chapters in the team reading group. In my experience both as a TA in my PhD program and in industry, that book is fairly easy to read through for anyone with solid understanding of linear algebra and vector calculus, which are freshman / sophomore level college math courses.

327 points by yarapavan 7y ago

Previous discussion from April 2018: https://news.ycombinator.com/item?id=16750789 https://news.ycombinator.com/item?id=16750789

mendeza 7y ago

I am taking CS 236 (Deep Generative Models) at Stanford and this course really helped me a lot in reviewing the math I needed for the class. This is because the chapters focus on the concepts and ideas you should know, so you don't have to waste time learning everything there is to know about linear algebra and convex optimization, but the essentials for machine learning.

Nicci00 7y ago

Id be useful to have a "math for programmers book" that uses pseudo code instead of math notation. I studied math notation in 8th grade and then forgot about it.

the_decider 7y ago
This book (Data Science Bookcamp) uses actual Python code instead of math notation. https://www.manning.com/books/data-science-bookcamp https://www.manning.com/books/data-science-bookcamp
TallGuyShort 7y ago
"Coding the matrix" was the breakthrough for me in grokking linear algebra, and this is what it does. Things are explained in terms of matrices and the mathematical transformations, and then explained in terms of python data structures and a loop over the elements. And most of the examples are computer science, like rotating images.
- uwuhn 7y ago
  I remember this course when it first came out, but didn't go through it since I didn't actually know how to program/code back then. Should I just buy the paperback off Amazon?
  - sn9 7y ago
    It's pretty cheap. I'd say go for it.
  - TallGuyShort 7y ago
    I didn't even know it was a course, I just got the book on Kindle. But I'd say go for it - as the other commenter said, it's cheap, and it doesn't require much coding knowledge, and it even explains most of what you do need to know if it's new to you. The real breakthrough is implementing the transformation in terms of fairly simple loops - which as a coder worked well for my brain. A non-coder might not find the advantage as big as I did, but I certainly don't think someone who can pick up some basic coding would struggle to understand what is being taught.
corysama 7y ago
Here's a start https://github.com/Jam3/math-as-code https://github.com/Jam3/math-as-code
mkl 7y ago
Possibly, but if you want to learn maths, then the notation is one of the smallest, easiest parts of it, and it's really helpful for the bigger, harder parts. Code is usually way more verbose than maths notation, so things get a lot bigger and it can be a lot harder to see what's going on. Learning maths notation is like learning the basic syntax of a programming language related to one you know already - there's not much to it and it doesn't take long to be able to read it comfortably. If you can already code then you know the basics and many relevant concepts already.
Impossible 7y ago
A Programmer's Introduction to Mathematics is probably what you're looking for. https://pimbook.org/ https://pimbook.org/
- ah700 7y ago
  I bought the book attempted to study from it and I am not a fan. It covers topics too briefly to be called an "introduction" to mathematics. If you have a solid math background and need a refresher you may find it useful, otherwise I found MIT OCW Mathematics for Computer Science to be a much more suitable introduction, and it comes with problem sets and answers (for the 2010 course). You can also purchase the course notes in book form on Amazon. https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/readings/ https://ocw.mit.edu/courses/electrical-engineering-and-compu... solutions https://drive.google.com/drive/folders/0B4G5KBKimr07WXRlT0VKb0E0TGc https://drive.google.com/drive/folders/0B4G5KBKimr07WXRlT0VK... physical book https://www.amazon.com/Mathematics-Computer-Science-Eric-Lehman/dp/1680921223/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=&sr=#customerReviews https://www.amazon.com/Mathematics-Computer-Science-Eric-Leh...
domnomnom 7y ago
If you can't even learn the syntax how will you ever learn the semantics?
ivan_ah 7y ago
Check out this short excerpt of definitions and examples of the math "alien symbols": https://minireference.com/static/excerpts/set_notation.pdf https://minireference.com/static/excerpts/set_notation.pdf They are really not that bad once you learn their meaning + very useful shorthand (you can think of math notation as a DSL with specific expressions for math operations). Longer preview of the book: https://minireference.com/static/excerpts/noBSguide_v5_preview.pdf https://minireference.com/static/excerpts/noBSguide_v5_previ... and here is another preview of the LA book: https://minireference.com/static/excerpts/noBSguide2LA_preview.pdf https://minireference.com/static/excerpts/noBSguide2LA_previ... Both books have been pretty popular with the programming crowd. They use standard math notation, but there are lots of code examples and computing analogies, so you'll feel right at home.

sergeyfilippov 7y ago

How would you compare this book to the first part of "Deep Learning" book (by Ian Goodfellow, Yoshua Bengio, and Aaron Courville)? https://www.amazon.com/gp/product/0262035618 https://www.amazon.com/gp/product/0262035618

zer0sugar 7y ago
I feel obligated to interject here as I have not read the book OP linked to but I have attempted to read the paper weight calling itself a book that you linked to. I have it right here actually. It's basically total trash. They claim to show you how to do the math but at the very best all they do is restate random formulas without any explanation. It's not even good enough to serve as a refresher if you know the math. It relies very heavily on you mentally decompiling mathematical notation. I can't believe I got fooled into buying that book. If you just want to learn the math there's no easier way than to pick up some math books from half price books. They're $10 a pop. It's an affordable way to learn at your own pace.
- random314 7y ago
  As a counterpoint, I have the book and found it to be really helpful.
  - disgruntledphd2 7y ago
    I enjoyed the book, but have a background in this area. I was amused by the suggestion that computer science undergrads could handle the book, as clearly the authors and I have met very different computer science undergrads.
    - mlthoughts2018 7y ago
      The Courville, Goodfellow and Bengio book is definitely suitable for undergraduates. In my current job, we often have new junior level (bachelor’s grads) ML hires work through that book and present chapters in the team reading group. In my experience both as a TA in my PhD program and in industry, that book is fairly easy to read through for anyone with solid understanding of linear algebra and vector calculus, which are freshman / sophomore level college math courses.