numerical-linear-algebra README

The project's README from github.com/fastai/numerical-linear-algebra. As one markdown file: README.md.

Computational Linear Algebra for Coders

This course is focused on the question: How do we do matrix computations with acceptable speed and acceptable accuracy?

This course was taught in the University of San Francisco's Masters of Science in Analytics program, summer 2017 (for graduate students studying to become data scientists). The course is taught in Python with Jupyter Notebooks, using libraries such as Scikit-Learn and Numpy for most lessons, as well as Numba (a library that compiles Python to C for faster performance) and PyTorch (an alternative to Numpy for the GPU) in a few lessons.

Accompanying the notebooks is a playlist of lecture videos, available on YouTube. If you are ever confused by a lecture or it goes too quickly, check out the beginning of the next video, where I review concepts from the previous lecture, often explaining things from a new perspective or with different illustrations, and answer questions.

Getting Help

You can ask questions or share your thoughts and resources using the Computational Linear Algebra category on our fast.ai discussion forums.

Table of Contents

The following listing links to the notebooks in this repository, rendered through the nbviewer service. Topics Covered:

0. Course Logistics (Video 1)

1. Why are we here? (Video 1)

We start with a high level overview of some foundational concepts in numerical linear algebra.

2. Topic Modeling with NMF and SVD (Video 2 and Video 3)

We will use the newsgroups dataset to try to identify the topics of different posts. We use a term-document matrix that represents the frequency of the vocabulary in the documents. We factor it using NMF, and then with SVD.

3. Background Removal with Robust PCA (Video 3, Video 4, and Video 5)

Another application of SVD is to identify the people and remove the background of a surveillance video. We will cover robust PCA, which uses randomized SVD. And Randomized SVD uses the LU factorization.

4. Compressed Sensing with Robust Regression (Video 6 and Video 7)

Compressed sensing is critical to allowing CT scans with lower radiation-- the image can be reconstructed with less data. Here we will learn the technique and apply it to CT images.

5. Predicting Health Outcomes with Linear Regressions (Video 8)

6. How to Implement Linear Regression(Video 8)

7. PageRank with Eigen Decompositions (Video 9 and Video 10)

We have applied SVD to topic modeling, background removal, and linear regression. SVD is intimately connected to the eigen decomposition, so we will now learn how to calculate eigenvalues for a large matrix. We will use DBpedia data, a large dataset of Wikipedia links, because here the principal eigenvector gives the relative importance of different Wikipedia pages (this is the basic idea of Google's PageRank algorithm). We will look at 3 different methods for calculating eigenvectors, of increasing complexity (and increasing usefulness!).

8. Implementing QR Factorization (Video 10)

Why is this course taught in such a weird order?

This course is structured with a top-down teaching method, which is different from how most math courses operate. Typically, in a bottom-up approach, you first learn all the separate components you will be using, and then you gradually build them up into more complex structures. The problems with this are that students often lose motivation, don't have a sense of the "big picture", and don't know what they'll need.

Harvard Professor David Perkins has a book, Making Learning Whole in which he uses baseball as an analogy. We don't require kids to memorize all the rules of baseball and understand all the technical details before we let them play the game. Rather, they start playing with a just general sense of it, and then gradually learn more rules/details as time goes on.

If you took the fast.ai deep learning course, that is what we used. You can hear more about my teaching philosophy in this blog post or this talk I gave at the San Francisco Machine Learning meetup.

All that to say, don't worry if you don't understand everything at first! You're not supposed to. We will start using some "black boxes" or matrix decompositions that haven't yet been explained, and then we'll dig into the lower level details later.

To start, focus on what things DO, not what they ARE.

numerical-linear-algebra (fastai/numerical-linear-algebra)

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Numerical-linear-algebra
What is this?A free online textbook of Jupyter notebooks teaching Computational Linear Algebra, built from a course taught at the University of San Francisco's Masters of Science in Analytics program in 2017.
Is this a coding library or a course?It is a set of Jupyter notebooks plus a linked YouTube lecture playlist, structured as a top-down textbook/course rather than installable software.
How is the content organized and where do I start?The README's Table of Contents links each notebook (rendered via nbviewer) in order from Course Logistics through Implementing QR Factorization, matching an 8-video lecture playlist; start at notebook 0 and follow the sequence.
What libraries do I need to run the notebooks?Mainly Scikit-Learn and Numpy, with Numba used for speed in some lessons and PyTorch used as a GPU-capable Numpy alternative in a few others.
Do I need to understand every method before I start?No — the course deliberately uses some matrix decompositions as 'black boxes' early on and explains the low-level details later, so it's normal not to understand everything at first.
Who is this course for?Graduate students studying to become data scientists, or anyone comfortable with Python who wants a practical, application-driven linear algebra course.
Why is the course taught in such an unusual order?It uses a top-down teaching method (like fast.ai's deep learning course) instead of the typical bottom-up math approach — students start applying decompositions in real problems and learn the underlying rules gradually, to stay motivated and see the big picture first.
What real-world problems does the course use to teach linear algebra?Topic modeling with NMF/SVD on newsgroup posts, background removal from surveillance video with Robust PCA, compressed sensing for CT scans, health outcome prediction with linear regression, and PageRank-style eigen decomposition on Wikipedia link data.
Are there accompanying video lectures?Yes, a full playlist of lecture videos is available on YouTube alongside the notebooks.
What are similar projects?100-Days-Of-ML-Code, mlcourse.ai, machine-learning-zoomcamp, autumn-recruitment, Book4_Power-of-Matrix, ailearning, d2l-en, d2l-zh
Which topics is it in?notebook, linear-algebra, scikit-learn, mathematics, numpy, curriculum, algorithms, course, jupyter notebook, academic-research, data-science, learning-resources
Creator
fastai
Size
62.5 MB
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11K
Updated
CommitJul 28
Age
9y
Commits · 90 Days