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Lectures: Tuesdays & Thursdays 2:00-3:20PM 📍WLH 2209

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Course description

This graduate course introduces the theory and methods of high-dimensional probability and statistics, focusing on tools for analyzing random phenomena in large-scale data and learning problems. Core topics include concentration inequalities, matrix concentration, entropy and transportation methods, chaining, and empirical processes. We will also highlight applications in statistics and machine learning, including regression and Lasso error bounds, covariance estimation and PCA, generalization in learning theory, and random projections.

Prerequisites: Probability theory and statistics (MATH 180A/B, DSC 212), multivariate calculus (MATH 10C), and linear algebra (MATH 18). Some exposure to statistics and machine learning is useful but not required.

Course information and schedule

Time and location: Tuesdays & Thursdays 2:00-3:20PM 📍WLH 2209

Instructor: Tianhao Wang, [email protected]

Office Hours: Thursdays 11AM-12PM 📍HDSI Room 455

🗓️ Schedule

Coursework

Coursework in this class will be centered on regular homework (90%) and classroom participation (10%). There will be no exams. Homework out each Tuesday and due at 11:59PM on the next Tuesday.

📄 Homework (90%)

Problem sets

🚨 Homework policy:

• Late submissions will not be accepted.
• Collaboration policy:
  • Students are encouraged to discuss general ideas and approaches with classmates.
  • However, all solutions must be written individually. Copying solutions from other students or online sources is not allowed.
  • If you discussed problems with classmates, please list their names on your submission.
• AI use policy:
  • Use of AI tools is strongly discouraged.
  • If any AI tool is used, details of its use must be provided in the submission, including the prompt and the model version and date.
  • Submitting answers directly generated by AI without your own understanding, verification, and significant rewriting is not acceptable.

💡 Participation (10%)