Difference between revisions of "Math 380: Mathematical Foundations of Data Science"

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(Created page with "== Catalog Information == === Title === Mathematical Foundations of Data Science === (Credit Hours:Lecture Hours:Lab Hours) === (3:3:0) === Offered === Contact Department...")
 
(→‎Minimal learning outcomes)
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=== Minimal learning outcomes ===
 
=== Minimal learning outcomes ===
 +
<div style="-moz-column-count:2; column-count:2;">
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# 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
 +
 +
</div>
  
 
=== Textbooks ===
 
=== Textbooks ===

Revision as of 09:01, 2 October 2024

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
      • 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:
      • Clustering
      • Prediction
      • Anomaly detection

Textbooks

Additional topics

Courses for which this course is prerequisite

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