Fall 2025

Published

24 September 2025

Meeting Schedule

We will meet biweekly on Mondays, 10:00AM-12:00PM, in HSPH 2-426.
Date Topic Reading Presenter
8th September tail and concentration bounds, uniform laws of large numbers Wainwright (2019): Ch. 2, 4 SB
22nd September metric entropy, minimax lower bounds Wainwright (2019): Ch. 5, 15 HL
6th October regularized regression and M-estimation Wainwright (2019): Ch. 7, 9 CT
20th October RKHS, non-parametric least squares Wainwright (2019): Ch. 12, 13 CJ
3rd November
17th November
1st December (FXB G03)
15th December

In the upcoming Fall term, we will tentatively discuss various topics in high-dimensional statistics, statistical learning theory and machine learning, with specific material drawn from and references made to the following texts: Wainwright (2019), Bickel and Doksum (2015), Hardt and Recht (2022), Bach (2024), and Duchi (2024). We will attempt to sample some of the following:

  • Wainwright (2019): Ch. 2 (tail and concentration bounds), 4 (uniform laws of large numbers), 5 (metric entropy), 7 (sparse linear models), 9 (regularized M-estimators), 12 (RKHS, including kernel ridge regression), 13 (non-parametric least squares), 15 (minimax lower bounds)
  • Bickel and Doksum (2015): Ch. 7 (tools for asymptotic analysis), 9 (inference in semi-parametric models), 12 (prediction and machine learning)
  • Hardt and Recht (2022): Ch. 3 (supervised learning), 5 (optimization), 6 (generalization), 7 (deep learning), 11 (sequential decision-making), 12 (reinforcement learning)
  • Duchi (2024): Ch. 2 (basics of information theory), 4 (concentration inequalities), 5 (generalization and stability), 8 (minimax lower bounds),
  • Bach (2024): Ch. 1 (mathematical preliminaries), 2 (supervised learning), 3 (linear least-squares), 4 (empirical risk minimization), 5 (optimization for machine learning), 7 (kernel methods), 8 (sparse methods)

References

Bach, Francis. 2024. Learning Theory from First Principles. https://www.di.ens.fr/%7Efbach/ltfp_book.pdf.
Bickel, Peter J, and Kjell A Doksum. 2015. Mathematical Statistics: Basic Ideas and Selected Topics, Volume II. CRC Press. https://doi.org/10.1201/b19822.
Duchi, John. 2024. Statistics and Information Theory. https://web.stanford.edu/class/stats311/lecture-notes.pdf.
Hardt, Moritz, and Benjamin Recht. 2022. Patterns, Predictions, and Actions: Foundations of Machine Learning. Princeton University Press.
Wainwright, Martin J. 2019. High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge University Press. https://doi.org/10.1017/9781108627771.