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MATH 637 (Fall 2023)
Mathematical Techniques in Data Science

• Course informations
  • Instructor: Vu Dinh (Ewing Hall 312)
  • Class times: MWF 11:30am-12:25am, Ewing Hall 207
  • Office hours:
    • Mondays 2:00pm-3:30pm (Ewing Hall 312)
    • Wednesdays 2:00pm-3:30pm (Ewing Hall 107A)
    • or by appointments.
  • Syllabus
  • Final project's info
  • Sample report (please acknowledge the authors of the report if you use the sample).
  • 2023 Mathematical Data Science Symposium

• Reference
  • An Introduction to Statistical Learning, James, Witten, Hastie, and Tibshirani.
    The pdf of the book is available for free at https://www.statlearning.com
  
  
  • The course provides an introduction to the fundamental techniques used in data science. The main objective of the course is to develop a good practical knowledge and a mathematical understanding of the common tools that are used to analyze modern datasets. The course also provides hands-on experience in data analysis through practical homework and class projects.

• Module 1: Introduction to supervised learning with scikit-learn and Keras
  • General information and Introduction
  • Python and Numpy demos; review of probability.
    Python Demo
    Numpy Demo
    Lecture 2
  • Nearest neighbors.
    Lecture 3
    k-Nearest Neighbors Demo
    k-Nearest Neighbors Practice
  • Logistic regression.
    Lecture 4
    Logistic Regression Demo
  • Feed-forward neural networks.
    Lecture 5
    Lab: Back-popagation and Gradient Descent
    
  • Deep learning with Keras
    Lecture 6
    MLP Keras Lab
    Link to Google Doc document
    
  • Convolutional neural networks.
    Lecture 7
    CNN Lab (template)
    Link to Goole Doc of the demo.

• Module 2: Mathematical techniques in data science
  • Statistical learning theory
    Lecture 8: Hypothesis spaces and loss functions ⊗ Cross-validation
    Demo: K-fold cross-validation
    Data for demo: hw4.csv
    Lecture 9: PAC Learning
    Note: A short introduction to statistical learning theory
    
  • Boosting
    Lecture 10: Decision trees; random forests; boosting
    
  • The kernel trick
    Lecture 11: SVMs
    Lecture 12: Clustering with kernel k-means
    
  • Shrinkage methods
    Lecture 13: Shrinkage methods for linear regression
    Lecture 14: Consistency of lasso
    Note: Variable selection consistency of lasso
    Further readings:
    
    • Zhao and Yu (2006)
    • Wainright (2009)
    • Sparsity, the lasso, and friends (Ryan Tibshirani)
  • Lecture 15: Manifold learning
    

• Assignments
  • Homework 1 (due 09/29)
    
  • Homework 2 (due 10/13)
    
  • Homework 3 (due 10/27)
    
  • Homework 4 (due 11/10)
    
  • Homework 5 (due 12/01)