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MATH 637 (Spring 2023)
Mathematical Techniques in Data Science

• Course informations
  • Instructor: Vu Dinh (Ewing Hall 312)
  • Class times: MW 5:00pm-6:15pm, Ewing Hall 207
  • Office hours:
    • Tuesdays 5:00pm-6:00pm, via Zoom
    • Wednesdays 3:30pm-4:30pm, Ewing Hall 312
    • or by appointments.
  • Syllabus
  • Final project's info
  • Sample report (please acknowledge the authors of the report if you use the sample).

• 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
  
  • Mon, 02/06: Lecture 1
  • Wed, 02/08: Python and Numpy demos; review of probability.
    Python Demo
    Numpy Demo
    Lecture 2
  • Mon, 02/13: Nearest neighbors.
    Lecture 3
    k-Nearest Neighbors Demo (template)
    k-Nearest Neighbors Demo (completed)
    k-Nearest Neighbors Practice
  • Wed, 02/15: Logistic regression.
    Lecture 4
    Logistic Regression (template)
    Logistic Regression (completed)
  • Mon, 02/20 and Wed, 02/22: Feed-forward neural networks.
    Lecture 5
    Feed-forward Neural Networks Demo (template)
    Feed-forward Neural Networks Demo (completed)
  • Mon, 02/27: Deep learning with Keras.
    Lecture 6
    MLP Keras Demo (template).
    Link to Goole Doc of the demo.
  • Wed, 03/01: Convolutional neural networks.
    Lecture 7
    CNN Demo (template).
    Link to Goole Doc of the demo.

• Module 2: Mathematical techniques in data science
  • Statistical learning theory
    Note: A short introduction to statistical learning theory
    Lecture 8: Hypothesis spaces and loss functions
    Hand-written notes: Updated Wed 03/15
    Lecture 9: Generalization bounds
    
  • The kernel trick
    Lecture 10: SVMs (Updated Mon 04/03)
    
  • Shrinkage methods
    Lecture 11: Linear regression, Lasso, and Cross-validation
    Demo: Lasso and K-fold cross-validation
    Lecture 12: Model consistency of lasso
    Note: Model consistency of lasso
    Further readings:
    
    • Zhao and Yu (2006).
    • Wainright (2009).
    • Sparsity, the lasso, and friends (Ryan Tibshirani).
  • Boosting
    Lecture 13: Decision trees; random forests; boosting
    Demo: Decision trees
    Demo: Ensemble methods
    
  • Other learning contexts
    Lecture 14: Principle component analysis (PCA)
    Lecture 15: Manifold learning
    Lecture 16: Clustering
    

• Assignments
  • Homework 1 (due 03/03)
    
  • Homework 2 (due 03/20)
    
  • Homework 3: This homework has two components. Due on 04/10.
    Homework 3 -- Written part
    Homework 3 -- Simulation part
    
  • Homework 4 (due 04/24)
    Data: hw4.csv
    
  • Homework 5 (due 05/08)