ORF 525: Statistical Foundations of Data Science

Spring Semester, 2025
MW 3:00 pm - 4:20 pm

Text BookDetails
Statistical Foundations of Data Science Book Cover
Fan, J., Li, R., Zhang, C.-H., and Zou (2020). 
Statistical Foundations of Data Science.
CRC Press. 

Homepage of the book 
To order the book from amazon.com or from CRC Press.

General Information

Instructor: Jianqing Fan, Frederick L. Moore'18 Professor of Finance.
Office: 205 Sherred Hall
Phone: 258-7924
E-mail: [email protected]

Office Hours: Monday 2:00 pm--3:00 pm (205 Sherred),  Tuesday 2:00pm--3:00pm (203b JRR, BCF), Wednesday 11:00am –- 12:00pm (203b JRR, BCF), or by appointments.

Precept: Arranged by the AI as needed

Assistants in Instruction (AIs):

  • Sange Tang, [email protected], 258-8787, Office: 222 Sherred Hall 
    • Office Hours and Locations.
      • Tuesday 3:00pm-4:00pm, Sherrerd Hall 123
      • Thursday 2:00pm-3:00pm, Sherrerd Hall 123
  • Financial Econometric Lab, 222 Sherred Hall, 258-9433
  • Statistics Lab, 213 Sherred Hall, 258-8787

Text Book

Reference Books

  • James, G., Witten, D., Hastie, T.J., Tibshirani, R. and Friedman, J. (2013). An Introduction to Statistical Learning with Applications in R . Springer, New York.
  • Hastie, T.J., Tibshirani, R. and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed). Springer, New York.
  • Buehlmann, P. and van de Geer, S. (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer, New York.
  • Hastie, T., Tibshirani, R., and Wainwright, M. (2015). Statistical learning with sparsity. CRC Press, New York.
  • Wainwright, M. J. (2019). High-dimensional statistics: A non-asymptotic viewpoint. Cambridge University Press.

Syllabus

This course gives an in-depth introduction to statistics and machine learning theory, methods, and algorithms for data science. It covers multiple regression, kernel learning, sparse regression, sure screening, generalized linear models and quasi-likelihood, supervised and unsupervised learning, deep learning, covariance learning and factor models, principal component analysis, and other related topics such as community detection, item ranking, topic modeling, and matrix completion. The applicability and limitations of these methods will be illustrated using mathematical statistics, a variety of modern real-world data sets, and manipulation of the statistical software R. 

Course material will cover the following topics; some will be assigned as reading materials.

  1. Rise of Big Data and Dimensionality*
    • Impact of Big Data;
    • Impact of Dimensionality
    • Aims of High-dimensional statistical learning
    • Aims of Big Data
    • Chapters 1--3
  2. Multiple and Nonparametric Regression
  3. Penalized Least Squares
    • Best subset and L_0 penalty
    • Folded-concave Penalized Least Squares
    • Lasso and L_1-regularization
    • Numerical Algorithms
    • Regularization parameters
    • Refitted Cross-validation
    • Extensions to Nonparametric Modeling
    • Lecture Notes 2, Homework 2
  4. Generalized Linear Models and Penalized Likelihood
    • Generalized Linear Models
    • Variable Selection via Penalized Likelihood
    • Numerical Algorithms
    • Statistical Properties
  5. Feature Screening
    • Correlation Screening
    • Generalized and Rank Correlation Screening
    • Nonparametric Screening
    • Sure Screening and False Selection
  6. Supervised Learning
    • Model-based Classifiers
    • Kernel Density Classifiers and Naive Bayes
    • Nearest Neighbor Classifiers
    • Classification Trees and Ensemble Classifiers 
    • Support Vector Machine
    • Sparsier classifiers
    • Sparse Discriminant Analysis
    • Sparse Additive Classifiers
  7. Unsupervised Learning
    • Cluster Analysis
    • Variable Selection in Clustering
    • Choice of Number of Clusters
    • Sparse PCA
  8. Introduction to Deep Learning
    • CNNs and RNNs
    • Transformers
    • Generative adversary networks
    • Training Algorithms
    • A Glimpse of Theory
  9. Covariance Regularization and Graphical Models
    • Sparse Covariance Matrix Estimation
    • Robust Covariance Inputs
    • Sparse Precision Matrix and Graphical Models
    • Latent Gaussian Graphical Models
  10. Covariance Learning and Factor Models
    • Principal Component Analysis
    • Factor Models and Structured Covariance Learning
    • Covariance and Precision Learning with Known Factors
    • Augmented Factor Models and Projected PCA
    • Asymptotic Properties
  11. Applications of PCA and Factor Models
    • Factor-adjusted Regularized Model Selection
    • Factor-adjusted Robust Multiple Testing
    • Augmented Factor Regression
    • Applications to Statistical Machine Learning

Computation

The software package for this class is R or RStudio. See R-labs below. Most of the computation in this class can be done through a laptop. Laptops with wireless communication turned off can be used during exams, and so are the calculators.

Attendance

Attendance of the class is required and essential.  The course materials are mainly from the notes.  Many conceptual issues and statistical thinking are only taught in the class. They will appear in the midterm and final exams.  

Homework

Problems will be assigned through Canvas approximately biweekly and submitted online. No late homework will be accepted. Missed homework will receive a grade of zero. The homework will be graded, and each assignment carries equal weight. You are allowed to work with other students on the homework problems; however, verbatim copying of homework is absolutely forbidden. Therefore, each student must ultimately produce his or her own homework to be handed in and graded.

Exams

There will be one in-class midterm exam and a final exam. All exams are required, and there will be no make-up exams. Missed exams will receive a grade of zero. All exams are open-book and open-notes. Laptops with wireless off and calculators may be used during the exams.

Schedules and Grading Policy

AssignmentSchedule
Homework (25%)Various due dates (approx 5 sets)
Midterm Exam (25%)Wednesday, March 19, 2025 (3:00pm--4:20pm, in class)
Final Exam (50%)9:30am--12:30pm, Friday, May 2, 2025 in Room 101, Sherred Hall

R-labs

The following files intend to help you become familiar with the use of R-lab commands.

Here are some useful materials, too.

Data Sets used in the class