Math 380: Mathematical Foundations of Data Science

Catalog Information

Title

Mathematical Foundations of Data Science

(Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

Offered

Contact Department

Prerequisite

Math 112

Description

Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.

Desired Learning Outcomes

Minimal learning outcomes

1. 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
   1. • 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
2. 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
3. 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:
   1. • Clustering
      • Prediction
      • Anomaly detection