Introduction to Numerical Linear Algebra for Coders
Numerical Linear Algebra for Coders is designed with a unique perspective: achieving matrix computations with both speed and accuracy. Originally part of the University of San Francisco's Masters of Science in Analytics program in 2017, this course is meticulously crafted for aspiring data scientists. Utilizing Python and Jupyter Notebooks, it incorporates powerful libraries such as Scikit-Learn and Numpy, with special appearances by Numba and PyTorch to enhance performance and GPU capabilities.
The course is supported by a series of lecture videos available on YouTube. These are particularly helpful as the instructor frequently reviews previous lessons, offering alternative explanations and visual aids which cater to different learning styles.
Course Structure and Resources
The course is delivered through a series of Jupyter Notebooks, which guide students through a comprehensive exploration of numerical linear algebra topics. Below is an overview of some major topics and course content:
Course Logistics
Students are introduced to the course logistics, covering the instructor's background, teaching methodologies, and the importance of technical writing. Resources for reviewing linear algebra concepts are also provided here to ensure foundational understanding.
Why Are We Here?
This section lays the groundwork by exploring fundamental concepts of numerical linear algebra. It covers matrix and tensor products, matrix decompositions, and vital considerations like accuracy, memory usage, speed, and the importance of parallelization and vectorization.
Topic Modeling with NMF and SVD
Students are introduced to topic modeling by using the newsgroups dataset. The course delves into constructing term-document matrices, applying Non-negative Matrix Factorization (NMF), and Singular Value Decomposition (SVD). Important tools and concepts such as TF-IDF, Stochastic Gradient Descent, and PyTorch are discussed.
Background Removal with Robust PCA
Here, robust Principal Component Analysis using SVD is explored through practical applications like video background removal. Concepts like L1 norm sparsity, robust PCA via primary component pursuit, and LU factorization are detailed along with a historical perspective on Gaussian Elimination.
Compressed Sensing with Robust Regression
Focused on how compressed sensing enables lower radiation in CT scans by reconstructing images with reduced data, this section provides insights into sparse matrices, L1 and L2 regression techniques, and robust regression techniques.
Predicting Health Outcomes with Linear Regressions
This section leverages linear regression techniques using Scikit-Learn. It covers polynomial features, numba-accelerated code for enhancing speed, and touches upon regularization and handling noise in datasets.
How to Implement Linear Regression
This practical segment delves into the workings behind Scikit-Learn’s linear regression implementations. It covers naive solutions, normal equations via Cholesky factorization, and various factorization techniques including QR and SVD, discussing the importance of stability and conditioning.
PageRank with Eigen Decompositions
The principles of SVD are expanded into eigen decomposition and its application in calculating PageRank, an algorithm that estimates page importance. Methods like the Power Method, QR Algorithm, and Arnoldi Iteration for finding eigenvectors are thoroughly examined.
Implementing QR Factorization
Exploring the QR factorization, this section demonstrates the methods of Gram-Schmidt and Householder transformations. Various examples point to the stability considerations critical in numerical computations.
Unique Teaching Approach
A distinctive feature of this course is its top-down approach, offering a holistic view before diving into the specifics. This method ensures students remain motivated by understanding the broader context of how each topic fits into the grand scheme of numerical linear algebra.
In conclusion, Numerical Linear Algebra for Coders presents a rich, hands-on exploration of matrix computations critical for data science students, providing them with the tools and understanding necessary for practical applications in computational environments.