Difference between revisions of "Math 380: Mathematical Foundations of Data Science"
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# Geometry and linear algebra in high-dimensional space | # Geometry and linear algebra in high-dimensional space | ||
| − | + | #* Working in high-dimensional space | |
| − | + | #* Intro to dimension reduction (including for visualization and computational necessity) | |
#* Johnson-Lindenstrauss | #* Johnson-Lindenstrauss | ||
#* SVD | #* SVD | ||
| − | # | + | #** For dimension reduction |
| − | + | #** For data compression | |
| − | + | #** PCA | |
| − | # | + | #** Use to solve the normal equation of OLS, even with collinearity |
#* More about eigenvalues and eigenvectors and their uses | #* More about eigenvalues and eigenvectors and their uses | ||
#* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups | #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups | ||
Revision as of 09:08, 2 October 2024
Contents
Catalog Information
Title
Mathematical Foundations of Data Science
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
Contact Department
Prerequisite
Description
Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.
Desired Learning Outcomes
Minimal learning outcomes
- Geometry and linear algebra in high-dimensional space
- Working in high-dimensional space
- Intro to dimension reduction (including for visualization and computational necessity)
- Johnson-Lindenstrauss
- SVD
- For dimension reduction
- For data compression
- PCA
- Use to solve the normal equation of OLS, even with collinearity
- More about eigenvalues and eigenvectors and their uses
- Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups
- Optimization
- Motivation: Overview of Machine Learning—it’s all just optimization and sampling
- Gradients and Hessians and what they tell us about the loss landscape
- Symbolic and automatic differentiation (sympy and autograd)
- Gradient descent
- Newton and Quasi-Newton
- Regularization
- Probabilistic Modeling
- Basic distributions, both discrete and continuous
- MLE is an optimization problem that usually cannot be solved analytically
- Use modeling and optimization skills to solve an interesting problem:
- Clustering
- Prediction
- Anomaly detection
