Welcome to the homepage of the
Variational Analysis and Statistical Theory Reading Group at CMU
Variational analysis, derived as an extension of classical real and convex analysis, deals with non-smooth optimization problems and perturbation analysis (i.e., how solutions change when the objective or estimating function is changed slightly).
The idea to use variational analysis for statistical theory is not new, but mostly forgotten. Starting from Chernoff (1954, Annals of Mathematical Statistics), several statisticians have used these tools to obtain asymptotic distribution results. Through this reading group, we learn more and derive reliable inference methods for irregular problems (including high-dimensional methods such as lasso or Dantzig selector).
Meeting Information
Unless otherwise notified, our regular weekly meeting for Fall 2025 is:
Mondays, 11:00–12:00 pm at BH 229A
Contact
To join our mailing list, please email: Woonyoung Chang or Kenta Takatsu at {woonyouc, ktakatsu}@andrew.cmu.edu.
Resources
Paper Suggestions & Presentation Sign-Up
Past meetings
| Meeting & Date | Presenter | Contents Cover |
|---|---|---|
| #1: August 25, 2025 | Arun Kuchibhotla |
Hjort and Pollard (2011), Kuchibhotla (2018, deterministic inequalities)
— Notes (PDF) |
| #2: September 1, 2025 | No Meeting | |
| #3: September 8, 2025 | Woonyoung Chang |
Basic concepts and results on epi-convergence of objective functions (with constraints) and set-convergence of argmin sets, along with their statistical applications
— Notes (PDF) |
| #4: September 15, 2025 | Woonyoung Chang |
Basic concepts in variational analysis, particularly focused on quantitative notions, including the epi-distance between functions and the truncated Hausdorff distance between sets. We will further discuss to derive quantitative bounds on a distance between argmin sets with some applications in statistics.
— Notes (PDF) |
| #5: September 22, 2025 | Kenta Takatsu |
In this session, I will prove quantitative bounds for inf f, the eps-arg min f, the arg min f, and level sets. I will then introduce the Kenmochi condition and prove bounds on the arg min set for constrained alpha-Hölder optimization problems, along with further examples such as constraint softening.
— Notes (PDF) |
| #6: September 29, 2025 | Kenta Takatsu |
We will host our seminar speaker, Professor Royset, for the first thirty minutes in a Q&A session. For the remaining thirty minutes, I will present a proof of the asymptotic normality of M-estimation under constraints, followed by a discussion on constraint quantification. I will also show how these quantifications can fail in the simple case of mean estimation on the boundary with a non-negativity constraint.
— Notes (PDF) |