Linear Algebra for Machine Learning

Linear algebra provides a mathematical framework for organizing information and then using that information to solve problems, especially physics, math, engineering, or data analytics problems. Linear algebra is essential for understanding and creating machine learning algorithms, especially neural network and deep learning models.

In this course, you will learn the linear algebra skills necessary for machine learning and neural network modelling. The course reviews the basic matrices and vector algebra as applied to linear systems and progresses into more advanced concepts of dimensionality reduction useful for Large Language models like GPT. The hands-on lessons and assignments will equip you with the mathematical background required to build and train simple neural networks.

The course begins with an introduction in neural networks and overview of the basic machine learning algorithms with simple practical examples to develop more intuitive understanding for machine learning models and why we need linear algebra. Subsequent sessions will present in detail principles of linear algebra with a sharp focus on the topics that will be useful in Machine Learning.

Key topics:

• Tensor operations and their role in data representation and early neural network models such as MLP
• Expressing systems of linear equations in matrix format and obtain the solution set, equivalent to calculating weights of neural network
• Calculate basis for a vector space, change of bases, used for text and image linear transformations: projection, mirroring
• Solving linear regression with matrix inversion of non-square matrices
• Continuous neural network optimization using gradient descent
• Singular value decomposition (with applications in image compression, reconstruction)
• Dimensionality reduction & principal component analysis
• Tensor flow 2 regression models

Practical experience:

• Hands-on lab assignments and projects using various open-source software programs (Octave/Python)

Course typically offered: Online, every quarter

Software: Students will use Octave/Python and TensorFlow to complete hands-on assignments and projects. These tools are free and open-source.

Prerequisites: Understanding of college-level algebra and calculus

Next steps: Upon completion, consider additional coursework in our specialized certificate in Machine Learning Methods to continue learning.

Contact: For more information about this course, please contact unex-techdata@ucsd.edu